statistics math homework

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High school statistics

Unit 1: displaying a single quantitative variable, unit 2: analyzing a single quantitative variable, unit 3: two-way tables, unit 4: scatterplots, unit 5: study design, unit 6: probability, unit 7: probability distributions & expected value.

Teach yourself statistics

Statistics and Probability

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Learn at your own pace. Free online tutorials cover statistics, probability, regression, analysis of variance, survey sampling, and matrix algebra - all explained in plain English.

• Advanced Placement (AP) Statistics . Full coverage of the AP Statistics curriculum.
• Probability . Fundamentals of probability. Clear explanations with pages of solved problems.
• Linear Regression . Regression analysis with one or more independent variables.
• ANOVA . Analysis of variance made easy. How to collect, analyze, and interpret data.
• Survey Sampling . How to conduct a statistical survey and analyze survey data.
• Matrix Algebra . Easy-to-understand introduction to matrix algebra.

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AP Statistics

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• AP Tutorial : Study our free, AP statistics tutorial to improve your skills in all test areas.
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1.1 Definitions of Statistics, Probability, and Key Terms

For each of the following eight exercises, identify: a. the population, b. the sample, c. the parameter, d. the statistic, e. the variable, and f. the data. Give examples where appropriate.

A fitness center is interested in the mean amount of time a client exercises in the center each week.

Ski resorts are interested in the mean age that children take their first ski and snowboard lessons. They need this information to plan their ski classes optimally.

A cardiologist is interested in the mean recovery period of her patients who have had heart attacks.

Insurance companies are interested in the mean health costs each year of their clients, so that they can determine the costs of health insurance.

A politician is interested in the proportion of voters in his district who think he is doing a good job.

A marriage counselor is interested in the proportion of clients she counsels who stay married.

Political pollsters may be interested in the proportion of people who will vote for a particular cause.

A marketing company is interested in the proportion of people who will buy a particular product.

Use the following information to answer the next three exercises: A Lake Tahoe Community College instructor is interested in the mean number of days Lake Tahoe Community College math students are absent from class during a quarter.

What is the population she is interested in?

• all Lake Tahoe Community College students
• all Lake Tahoe Community College English students
• all Lake Tahoe Community College students in her classes
• all Lake Tahoe Community College math students

Consider the following:

X X = number of days a Lake Tahoe Community College math student is absent

In this case, X is an example of a:

• population.

The instructor’s sample produces a mean number of days absent of 3.5 days. This value is an example of a:

1.2 Data, Sampling, and Variation in Data and Sampling

For the following exercises, identify the type of data that would be used to describe a response (quantitative discrete, quantitative continuous, or qualitative), and give an example of the data.

number of tickets sold to a concert

percent of body fat

favorite baseball team

time in line to buy groceries

number of students enrolled at Evergreen Valley College

most-watched television show

brand of toothpaste

distance to the closest movie theatre

age of executives in Fortune 500 companies

number of competing computer spreadsheet software packages

Use the following information to answer the next two exercises: A study was done to determine the age, number of times per week, and the duration (amount of time) of resident use of a local park in San Jose. The first house in the neighborhood around the park was selected randomly and then every 8th house in the neighborhood around the park was interviewed.

“Number of times per week” is what type of data?

• qualitative
• quantitative discrete
• quantitative continuous

“Duration (amount of time)” is what type of data?

Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. Suppose an airline conducts a survey. Over Thanksgiving weekend, it surveys six flights from Boston to Salt Lake City to determine the number of babies on the flights. It determines the amount of safety equipment needed by the result of that study.

• Using complete sentences, list three things wrong with the way the survey was conducted.
• Using complete sentences, list three ways that you would improve the survey if it were to be repeated.

Suppose you want to determine the mean number of students per statistics class in your state. Describe a possible sampling method in three to five complete sentences. Make the description detailed.

Suppose you want to determine the mean number of cans of soda drunk each month by students in their twenties at your school. Describe a possible sampling method in three to five complete sentences. Make the description detailed.

List some practical difficulties involved in getting accurate results from a telephone survey.

List some practical difficulties involved in getting accurate results from a mailed survey.

With your classmates, brainstorm some ways you could overcome these problems if you needed to conduct a phone or mail survey.

The instructor takes her sample by gathering data on five randomly selected students from each Lake Tahoe Community College math class. The type of sampling she used is

• cluster sampling
• stratified sampling
• simple random sampling
• convenience sampling

A study was done to determine the age, number of times per week, and the duration (amount of time) of residents using a local park in San Jose. The first house in the neighborhood around the park was selected randomly and then every eighth house in the neighborhood around the park was interviewed. The sampling method was:

• simple random

Name the sampling method used in each of the following situations:

• A woman in the airport is handing out questionnaires to travelers asking them to evaluate the airport’s service. She does not ask travelers who are hurrying through the airport with their hands full of luggage, but instead asks all travelers who are sitting near gates and not taking naps while they wait.
• A teacher wants to know if her students are doing homework, so she randomly selects rows two and five and then calls on all students in row two and all students in row five to present the solutions to homework problems to the class.
• The marketing manager for an electronics chain store wants information about the ages of its customers. Over the next two weeks, at each store location, 100 randomly selected customers are given questionnaires to fill out asking for information about age, as well as about other variables of interest.
• The librarian at a public library wants to determine what proportion of the library users are children. The librarian has a tally sheet on which she marks whether books are checked out by an adult or a child. She records this data for every fourth patron who checks out books.
• A political party wants to know the reaction of voters to a debate between the candidates. The day after the debate, the party’s polling staff calls 1,200 randomly selected phone numbers. If a registered voter answers the phone or is available to come to the phone, that registered voter is asked whom he or she intends to vote for and whether the debate changed his or her opinion of the candidates.

A “random survey” was conducted of 3,274 people of the “microprocessor generation” (people born since 1971, the year the microprocessor was invented). It was reported that 48% of those individuals surveyed stated that if they had $2,000 to spend, they would use it for computer equipment. Also, 66% of those surveyed considered themselves relatively savvy computer users.

• Do you consider the sample size large enough for a study of this type? Why or why not?
• Based on your “gut feeling,” do you believe the percents accurately reflect the U.S. population for those individuals born since 1971? If not, do you think the percents of the population are actually higher or lower than the sample statistics? Why? Additional information: The survey, reported by Intel Corporation, was filled out by individuals who visited the Los Angeles Convention Center to see the Smithsonian Institute's road show called “America’s Smithsonian.”
• With this additional information, do you feel that all demographic and ethnic groups were equally represented at the event? Why or why not?
• With the additional information, comment on how accurately you think the sample statistics reflect the population parameters.

The Well-Being Index is a survey that follows trends of U.S. residents on a regular basis. There are six areas of health and wellness covered in the survey: Life Evaluation, Emotional Health, Physical Health, Healthy Behavior, Work Environment, and Basic Access. Some of the questions used to measure the Index are listed below.

Identify the type of data obtained from each question used in this survey: qualitative, quantitative discrete, or quantitative continuous.

• Do you have any health problems that prevent you from doing any of the things people your age can normally do?
• During the past 30 days, for about how many days did poor health keep you from doing your usual activities?
• In the last seven days, on how many days did you exercise for 30 minutes or more?
• Do you have health insurance coverage?

In advance of the 1936 Presidential Election, a magazine titled Literary Digest released the results of an opinion poll predicting that the republican candidate Alf Landon would win by a large margin. The magazine sent post cards to approximately 10,000,000 prospective voters. These prospective voters were selected from the subscription list of the magazine, from automobile registration lists, from phone lists, and from club membership lists. Approximately 2,300,000 people returned the postcards.

• Think about the state of the United States in 1936. Explain why a sample chosen from magazine subscription lists, automobile registration lists, phone books, and club membership lists was not representative of the population of the United States at that time.
• What effect does the low response rate have on the reliability of the sample?
• Are these problems examples of sampling error or nonsampling error?
• During the same year, George Gallup conducted his own poll of 30,000 prospective voters. These researchers used a method they called "quota sampling" to obtain survey answers from specific subsets of the population. Quota sampling is an example of which sampling method described in this module?

Crime-related and demographic statistics for 47 US states in 1960 were collected from government agencies, including the FBI's Uniform Crime Report . One analysis of this data found a strong connection between education and crime indicating that higher levels of education in a community correspond to higher crime rates.

Which of the potential problems with samples discussed in 1.2 Data, Sampling, and Variation in Data and Sampling could explain this connection?

YouPolls is a website that allows anyone to create and respond to polls. One question posted April 15 asks:

“Do you feel happy paying your taxes when members of the Obama administration are allowed to ignore their tax liabilities?” (lastbaldeagle. 2013. On Tax Day, House to Call for Firing Federal Workers Who Owe Back Taxes. Opinion poll posted online at: http://www.youpolls.com/details.aspx?id=12328 (accessed May 1, 2013).)

As of April 25, 11 people responded to this question. Each participant answered “NO!”

Which of the potential problems with samples discussed in this module could explain this connection?

A scholarly article about response rates begins with the following quote:

“Declining contact and cooperation rates in random digit dial (RDD) national telephone surveys raise serious concerns about the validity of estimates drawn from such research.”(Scott Keeter et al., “Gauging the Impact of Growing Nonresponse on Estimates from a National RDD Telephone Survey,” Public Opinion Quarterly 70 no. 5 (2006), http://poq.oxfordjournals.org/content/70/5/759.full (accessed May 1, 2013).)

The Pew Research Center for People and the Press admits:

“The percentage of people we interview – out of all we try to interview – has been declining over the past decade or more.” (Frequently Asked Questions, Pew Research Center for the People & the Press, http://www.people-press.org/methodology/frequently-asked-questions/#dont-you-have-trouble-getting-people-to-answer-your-polls (accessed May 1, 2013).)

• What are some reasons for the decline in response rate over the past decade?
• Explain why researchers are concerned with the impact of the declining response rate on public opinion polls.

1.3 Frequency, Frequency Tables, and Levels of Measurement

Fifty part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:

• Fill in the blanks in Table 1.33 .
• What percent of students take exactly two courses?
• What percent of students take one or two courses?

Sixty adults with gum disease were asked the number of times per week they used to floss before their diagnosis. The (incomplete) results are shown in Table 1.34 .

• Fill in the blanks in Table 1.34 .
• What percent of adults flossed six times per week?
• What percent flossed at most three times per week?

Nineteen immigrants to the U.S were asked how many years, to the nearest year, they have lived in the U.S. The data are as follows: 2 ; 5 ; 7 ; 2 ; 2 ; 10 ; 20 ; 15 ; 0 ; 7 ; 0 ; 20 ; 5 ; 12 ; 15 ; 12 ; 4 ; 5 ; 10 .

Table 1.35 was produced.

• Fix the errors in Table 1.35 . Also, explain how someone might have arrived at the incorrect number(s).
• Explain what is wrong with this statement: “47 percent of the people surveyed have lived in the U.S. for 5 years.”
• Fix the statement in b to make it correct.
• What fraction of the people surveyed have lived in the U.S. five or seven years?
• What fraction of the people surveyed have lived in the U.S. at most 12 years?
• What fraction of the people surveyed have lived in the U.S. fewer than 12 years?
• What fraction of the people surveyed have lived in the U.S. from five to 20 years, inclusive?

How much time does it take to travel to work? Table 1.36 shows the mean commute time by state for workers at least 16 years old who are not working at home. Find the mean travel time, and round off the answer properly.

Forbes magazine published data on the best small firms in 2012. These were firms which had been publicly traded for at least a year, have a stock price of at least $5 per share, and have reported annual revenue between $5 million and $1 billion. Table 1.37 shows the ages of the chief executive officers for the first 60 ranked firms.

• What is the frequency for CEO ages between 54 and 65?
• What percentage of CEOs are 65 years or older?
• What is the relative frequency of ages under 50?
• What is the cumulative relative frequency for CEOs younger than 55?
• Which graph shows the relative frequency and which shows the cumulative relative frequency?

Use the following information to answer the next two exercises: Table 1.38 contains data on hurricanes that have made direct hits on the U.S. Between 1851 and 2004. A hurricane is given a strength category rating based on the minimum wind speed generated by the storm.

What is the relative frequency of direct hits that were category 4 hurricanes?

• Not enough information to calculate

What is the relative frequency of direct hits that were AT MOST a category 3 storm?

1.4 Experimental Design and Ethics

How does sleep deprivation affect your ability to drive? A recent study measured the effects on 19 professional drivers. Each driver participated in two experimental sessions: one after normal sleep and one after 27 hours of total sleep deprivation. The treatments were assigned in random order. In each session, performance was measured on a variety of tasks including a driving simulation.

Use key terms from this module to describe the design of this experiment.

An advertisement for Acme Investments displays the two graphs in Figure 1.14 to show the value of Acme’s product in comparison with the Other Guy’s product. Describe the potentially misleading visual effect of these comparison graphs. How can this be corrected?

The graph in Figure 1.15 shows the number of complaints for six different airlines as reported to the US Department of Transportation in February 2013. Alaska, Pinnacle, and Airtran Airlines have far fewer complaints reported than American, Delta, and United. Can we conclude that American, Delta, and United are the worst airline carriers since they have the most complaints?

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Statistics and Probability Worksheets

Welcome to the statistics and probability page at Math-Drills.com where there is a 100% chance of learning something! This page includes Statistics worksheets including collecting and organizing data, measures of central tendency (mean, median, mode and range) and probability.

Students spend their lives collecting, organizing, and analyzing data, so why not teach them a few skills to help them on their way. Data management is probably best done on authentic tasks that will engage students in their own learning. They can collect their own data on topics that interest them. For example, have you ever wondered if everyone shares the same taste in music as you? Perhaps a survey, a couple of graphs and a few analysis sentences will give you an idea.

Statistics has applications in many different fields of study. Budding scientists, stock market brokers, marketing geniuses, and many other pursuits will involve managing data on a daily basis. Teaching students critical thinking skills related to analyzing data they are presented will enable them to make crucial and informed decisions throughout their lives.

Probability is a topic in math that crosses over to several other skills such as decimals, percents, multiplication, division, fractions, etc. Probability worksheets will help students to practice all of these skills with a chance of success!

Most Popular Statistics and Probability Worksheets this Week

Mean, Median, Mode and Range Worksheets

Calculating the mean, median, mode and range are staples of the upper elementary math curriculum. Here you will find worksheets for practicing the calculation of mean, median, mode and range. In case you're not familiar with these concepts, here is how to calculate each one. To calculate the mean, add all of the numbers in the set together and divide that sum by the number of numbers in the set. To calculate the median, first arrange the numbers in order, then locate the middle number. In sets where there are an even number of numbers, calculate the mean of the two middle numbers. To calculate the mode, look for numbers that repeat. If there is only one of each number, the set has no mode. If there are doubles of two different numbers and there are more numbers in the set, the set has two modes. If there are triples of three different numbers and there are more numbers in the set, the set has three modes, and so on. The range is calculated by subtracting the least number from the greatest number.

Note that all of the measures of central tendency are included on each page, but you don't need to assign them all if you aren't working on them all. If you're only working on mean, only assign students to calculate the mean.

In order to determine the median, it is necessary to have your numbers sorted. It is also helpful in determining the mode and range. To expedite the process, these first worksheets include the lists of numbers already sorted.

• Calculating Mean, Median, Mode and Range from Sorted Lists Sets of 5 Numbers from 1 to 10 Sets of 5 Numbers from 10 to 99 Sets of 5 Numbers from 100 to 999 Sets of 10 Numbers from 1 to 10 Sets of 10 Numbers from 10 to 99 Sets of 10 Numbers from 100 to 999 Sets of 20 Numbers from 10 to 99 Sets of 15 Numbers from 100 to 999

Normally, data does not come in a sorted list, so these worksheets are a little more realistic. To find some of the statistics, it will be easier for students to put the numbers in order first.

• Calculating Mean, Median, Mode and Range from Unsorted Lists Sets of 5 Numbers from 1 to 10 Sets of 5 Numbers from 10 to 99 Sets of 5 Numbers from 100 to 999 Sets of 10 Numbers from 1 to 10 Sets of 10 Numbers from 10 to 99 Sets of 10 Numbers from 100 to 999 Sets of 20 Numbers from 10 to 99 Sets of 15 Numbers from 100 to 999

Collecting and Organizing Data

Teaching students how to collect and organize data enables them to develop skills that will enable them to study topics in statistics with more confidence and deeper understanding.

• Constructing Line Plots from Small Data Sets Construct Line Plots with Smaller Numbers and Lines with Ticks Provided (Small Data Set) Construct Line Plots with Smaller Numbers and Lines Only Provided (Small Data Set) Construct Line Plots with Smaller Numbers (Small Data Set) Construct Line Plots with Larger Numbers and Lines with Ticks Provided (Small Data Set) Construct Line Plots with Larger Numbers and Lines Only Provided (Small Data Set) Construct Line Plots with Larger Numbers (Small Data Set)
• Constructing Line Plots from Larger Data Sets Construct Line Plots with Smaller Numbers and Lines with Ticks Provided Construct Line Plots with Smaller Numbers and Lines Only Provided Construct Line Plots with Smaller Numbers Construct Line Plots with Larger Numbers and Lines with Ticks Provided Construct Line Plots with Larger Numbers and Lines Only Provided Construct Line Plots with Larger Numbers

Interpreting and Analyzing Data

Answering questions about graphs and other data helps students build critical thinking skills. Standard questions include determining the minimum, maximum, range, count, median, mode, and mean.

• Answering Questions About Stem-and-Leaf Plots Stem-and-Leaf Plots with about 25 data points Stem-and-Leaf Plots with about 50 data points Stem-and-Leaf Plots with about 100 data points
• Answering Questions About Line Plots Line Plots with Smaller Data Sets and Smaller Numbers Line Plots with Smaller Data Sets and Larger Numbers Line Plots with Larger Data Sets and Smaller Numbers Line Plots with Larger Data Sets and Larger Numbers
• Answering Questions About Broken-Line Graphs Answer Questions About Broken-Line Graphs
• Answering Questions About Circle Graphs Circle Graph Questions (Color Version) Circle Graph Questions (Black and White Version) Circle Graphs No Questions (Color Version) Circle Graphs No Questions (Black and White Version)
• Answering Questions About Pictographs Answer Questions About Pictographs

Probability Worksheets

• Calculating Probabilities with Dice Sum of Two Dice Probabilities Sum of Two Dice Probabilities (with table)

Spinners can be used for probability experiments or for theoretical probability. Students should intuitively know that a number that is more common on a spinner will come up more often. Spinning 100 or more times and tallying the results should get them close to the theoretical probability. The more sections there are, the more spins will be needed.

• Calculating Probabilities with Number Spinners Number Spinner Probability (4 Sections) Number Spinner Probability (5 Sections) Number Spinner Probability (6 Sections) Number Spinner Probability (7 Sections) Number Spinner Probability (8 Sections) Number Spinner Probability (9 Sections) Number Spinner Probability (10 Sections) Number Spinner Probability (11 Sections) Number Spinner Probability (12 Sections)

Non-numerical spinners can be used for experimental or theoretical probability. There are basic questions on every version with a couple extra questions on the A and B versions. Teachers and students can make up other questions to ask and conduct experiments or calculate the theoretical probability. Print copies for everyone or display on an interactive white board.

• Probability with Single-Event Spinners Animal Spinner Probability ( 4 Sections) Animal Spinner Probability ( 5 Sections) Animal Spinner Probability ( 10 Sections) Letter Spinner Probability ( 4 Sections) Letter Spinner Probability ( 5 Sections) Letter Spinner Probability ( 10 Sections) Color Spinner Probability ( 4 Sections) Color Spinner Probability ( 5 Sections) Color Spinner Probability ( 10 Sections)
• Probability with Multi-Event Spinners Animal/Letter Combined Spinner Probability ( 4 Sections) Animal/Letter Combined Spinner Probability ( 5 Sections) Animal/Letter Combined Spinner Probability ( 10 Sections) Animal/Letter/Color Combined Spinner Probability ( 4 Sections) Animal/Letter/Color Combined Spinner Probability ( 5 Sections) Animal/Letter/Color Combined Spinner Probability ( 10 Sections)

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Step-by-Step Statistics Solutions

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8: Statistics

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• 8.1: Introduction
• 8.2: Gathering and Organizing Data
• 8.3: Visualizing Data
• 8.4: Mean, Median and Mode
• 8.5: Range and Standard Deviation
• 8.6: Percentiles
• 8.7: The Normal Distribution
• 8.8: Applications of the Normal Distribution
• 8.9: Scatter Plots, Correlation, and Regression Lines
• 8.10.1: Key Terms
• 8.10.2: Key Concepts
• 8.10.3: Videos
• 8.10.4: Formula Review
• 8.10.5: Projects
• 8.10.6: Chapter Review
• 8.10.7: Chapter Test

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This in depth and meaty tutorial will help you understand how to factor algebraic expressions .

Simplifying radicals gotta be THE most useful thing to know about in Basic Algebra. Learn about it in this tutorial .

Among all things related to the rules of exponents, students tend to get confused when dealing with negative exponents . This tutorial will clarify all your doubts.

One of the crucial skills required to deal with algebraic expression is the proper use of rules of exponents .

All you need to know about Cramer's Rule and how to use it to solve systems of linear equations.

See this tutorial to learn how to and when to use the mean, median or mode as the measure of center, depending on the type of distribution.

What is a Box and Whisker Plot? How do you define the box? The Whiskers? Find out in this tutorial .

And to conclude the series on conic sections, it is now time for the ellipse .

We continue our series of tutorial on conic sections. This time, it is the turn of the hyperbola .

Conic sections and the general equation of the parabola .

A very complete and in depth tutorial on partial fractions decompositions , with concrete steps to follow.

A complete tutorial of how to apply log rules , with explanations and examples.

Take a look at this tutorial about PEMDAS and the convention for the order of operations .

Learn more about all the concepts related with the graph of a function .

One of the most versatile Math artifacts: See how the unit circle crosses Algebra, Geometry and Trigonometry.

Crucial concepts when dealing with functions: Domain and Range .

Another great, in-depth tutorial. All you need to know about the Absolute Value of a number .

Here is another crucial property in Algebra: the Commutative Property .

The associative property is one of those properties that is used all the time, but we do not really know.

All there is to know about horizontal asymptotes .

Learn all that there is to the circle: The Equation of a Circle .

We have started a new section for Finance solvers. Check them out: Future Value Calculator , Present Value Calculator , Present Value of an Annuity , among many other Finance Calculators .

One of the best advice right before starting a new semester: Don't panic .

Excellent article about why it is usually the easy Stats classes those where students need the most help with. Check it out! .

Going for a large overhaul in the site, which much more powerful tools. In the meantime, here I leave you a new article Tricks of the Trade: Finding Stats Homework Help . Another interesting post about why more and more students end up learning their Stats using private tutors. Check it here . Also all, you need to know about the process finding help with your finance assignment .

Although we already had a complete descriptive statistics calculator , I have requests to make some specific calculators, to compute one measure at a time, so here I have it: I added a mean calculator , standard deviation calculator and median calculator .

I have added a page that puts together all the articles we have available about education topics . Also, I found this interesting article about the advantages of staring with Algebra early in life.

Check our revised SPSS tutorial .

I have added a couple of algebraic solvers for arithmetic sequences and geometric sequences .

Z-scores are the way we compute normal probabilities, as any general normal distribution can always be reduced to a standard normal distribution. Check out this Z-Scores Calculator .

I have found two excellent tutorials one about hypothesis testing , and the other one about statistics and parameters . Both are great reads.

I have added several effect size calculators, including a Gamma Calculator and a Phi Coefficient Calculator .

The idea of "effect size" is very relevant in statistics. If often happens that a test statistics is significant, but the association has no practical meaning. This is because a extremely large sample size alone can find significant n extremely small effect. Cramer's V is a statistic that assess the effect size or practical significance of the association between nominal variables. Check it out: Cramer's V Calculator .

More solvers for our series of elementary geometry solvers, and we now add a calculator of the area and volume of a square pyramid that will show you all the steps and formulas used to calculate the surface area and volume of a square pyramid of side \(l\) and height \(h\).

Keeping the momentum up, here you have a calculator of the area and volume of a cone that will show you all the steps and formulas used to calculate the area and volume of a right circle cone radius \(r\) and height \(h\).

Another solver for our Geometry series, a calculator of the area and volume of a sphere that will show you all the steps and formulas used to calculate the area and volume of a sphere of radius \(r\).

Typically found in special tables, here you have a critical correlation calculator . The advantage of this calculator is that it will compute the critical correlation for any value of \(n\), which is not always possible when you use critical correlation tables, which only have a few values of \(n\).

Lots of people were asking for geometry solvers and here they are. I have started a new section for Geometry and I'll be adding more solver on a continuous basis. For now, here I leave for you a area and perimeter of a circle calculator , and an area and volume calculator for cylinders

This one is a solver that user were clamoring for: Let me introduce our Polynomial Operations Calculator , with which you can add, subtract and multiply polynomials, with the solution shown step-by-step. Also, we have started with MathQuill, and excellent option for enhancing the input of math.

We expand even more our Algebra series with some more basic solvers, in this case, a absolute value calculator .

New solver in our Algebra series, now I have added a solver that evaluates all sort of algebraic expressions that can include any kind of operation (sum, subtraction, multiplication, division), numbers, fractions, trigonometric functions, exponential functions, powers, roots, etc. Check our Algebraic Expression Calculator .

Continuing the series of Algebra solvers, I have added a solver that calculates operations between fractions and shows all the steps. Depending of the operation required it conducts the appropriate steps to reach the final fraction result, in reduced form. Check out our fraction operation solver .

I have made a new function grapher to replace the old flash grapher we had. This time, I used the Google Chart format, that looks more modern and goes along the trend of JS charts.

I get a lots of requests for this one, so here it goes. This is a fraction reduction tool fraction-reduction-lowest-terms.php , that takes a fraction into its lowest terms.

This time, I added a greatest common divisor , or as it usually known as greatest common factor calculator . I took care to provide as much detail as possible in the calculations shown by the solver.

Today I start with a new series of Algebra solvers. I have added a prime decomposition calculator , you type in a positive integer number and the solver tell you in a detailed way what is its prime decomposition.

I am very pleased to announce that we have rolled a new site design, with a much improved mobile functionality.

This time I decided to write on functions and how to deal with them .

Another article. This time dealing with the possibility of having a software that can solve Math and Stats problems FULLY automatically Check Here .

I loved the feedback I got from the first Math Crack, so I decided to pump up the series. I'll be uploading them periodically. This next first Math Crack is about an easy explanation of derivatives .

I finally started a project that I have been wanting to undertake for a while. It is the Math Cracks, which is the way I call to this short tutorials that attempt to explain hard math concepts in simple terms, step-by-step. The first Math Crack of the series is Integration by Parts .

A site update is coming soon. I will be changing the layout a bit so that to keep the solvers in a more organized way and the articles will be organized rather in blog format. I will be adding a complete set of Algebra solvers, so stay tuned.

A couple of tutorials and solvers were added: Quadratic Formula: The meaning of the term -b/2a , an article about Algebra 2 and a Line Plot Maker

I have added a couple of new articles for your reading enjoyment: Math Articles

I have added a minimum sample size calculator for mean and proportion

After long working hours, I've finished all the solvers required to cover all basic statistics topics. The new solvers are: Z-test for two means , Z-test for two proportions , T-test for two means , T-test for paired samples , Chi-Square Goodness of fit , and Chi-Square test of Independence . I also added the most important non-parametric tests, which are the Sign Test , also Wilcoxon Signed Ranks Test , as well as the Wilcoxon Rank-Sum Test and Kruskal-Wallis

I get asked to review different online curricula. Thanks to a guest writer, I just added a great article about online accounting curricula. You can check it here .

Found a very informational article about the do's and dont's of Accounting Homework Help. You can check it here .

Great changes to improve user experience are coming very soon. I have written recently many math and stats solvers that I'll be adding to the site. I've been polishing the scripts we already have and this is almost turning into a full time job. As many users are aware, we have had ads for the last few months, and even though I don't like ads, it is the only way to support the site, which is turning into a full time job by now. I'm looking for a more efficient way of using ads so that the site can be ad-supported and it continue being free that way.

More Stats tests done. I have finished a t-test for one population mean with unknown population standard deviation and a Chi-Square test for one population variance . Pretty much as the other solvers I have added, they are simple to use: define hypotheses, and parameters of the test, and a detailed step-by-step calculation is performed.

I've been working on these for a while and I finally finished them. I added a z-test for one population mean and a z-test for one population proportion . Very user friendly, define hypotheses, and parameters of the test, and a detailed step-by-step calculation is performed. Recommended.

I just added a working histogram maker . You enter the dataset and the number of bins and a properly scaled histogram is rendered by the script.

I have added a very cool bar graph maker . You enter the categories, the values associated with each of the categories, and a bar chart rendered by the script.

Not exactly the typical calculator we do, but I have had some requests for it, so I added a simple mortgage calculator tool to compute the monthly payment for a mortgage, under basic assumptions (without considering PMI and insurance).

I have uploaded a 2x2 system of linear equations solver.

I have updated the pie chart maker script.

I have added two confidence interval calculators. They are confidence intervals for the population mean μ when the population standard deviation σ is known and for when the and a population standard deviation is not known .

We have two more probability calculators. They are a binomial distribution calculator and a Poisson distribution calculator .

I have added two new probability calculators, based on a couple of requests I had. They are a exponential distribution calculator and a uniform distribution calculator .

I have added a new article. Check it out here .

I have added a correlation coefficient calculator . This time, the script is more user friendly, and checks for errors in the data before processing them.

I received a whole lot of e-mails asking for a tool to calculate grades. Well, I just did it. With this online grade calculator you are able to input your assignment/test scores and the calculator will tell your final score and final letter grade. And if you don't have all the grades, the calculator will tell you what score you need to get in your final assignment/test in order to get an A.

After some time of silence, I'm back. As many of you know, I run this site on my spare time trying to keep it as updated as possible. I'm very pleased to see the positive effect the math tools we offer in our site are having in the community. Countless e-mails thanking me for the work I put in the site make me want to keep working even harder. The free online math calculator we provide in the site have even been used as references in scientific papers. That is very cool indeed! I have great plans for the site. Keep visiting.

Our good friends at MGT are giving specially for us this 15% discount code for their online math homework help services: mthcrk1501 . From references given by users of our community, they are very reliable.

Summer is over, and time is back for some math. We have great plans for this year. Our aim is to offer the best quality free math help, for which reason we will continue adding more and more useful content. We also expect to materialize some very interesting partnerships. Stay tuned!

As promised, a couple of critical values calculators have been added: z-distribution critical values and t-distribution critical values

A t-distribution probability calculator was added. This is the first delivery of a series of scripts that will be added. Coming soon a couple of online calculators for critical values for the z-distribution and the t-distribution.

I just added an article about math problem solving techniques. See article

We have added more than 300 solved statistics problems

Due to a problem with a configuration file the scripts in the site were not working for a while, now they are working fine. Sorry for the inconvenience.

A good tutorial about the normal distribution was added. The normal distribution and the standard normal distribution

I added a good list of solved statistics problems.

I made a few adjustments to the scatterplot module, and added a new regression line tool, to complement the existing tool. Linear Regression Calculator

This new resource seems to be very useful, you may find it interesting to take a look Free Statistics Help

The site is back up online. For problems out of my control the site was down for a couple of weeks. We'll be back with new material. Thanks to everyone.

I have found a good collection of free solved math problems and math answers.

In case you have any suggestion, please do not hesitate to contact us .

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• Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Number Line Mean, Median & Mode
• Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Interval Notation Pi (Product) Notation Induction Logical Sets Word Problems
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• Trigonometry Identities Proving Identities Trig Equations Trig Inequalities Evaluate Functions Simplify
• Statistics Mean Geometric Mean Quadratic Mean Average Median Mode Order Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution
• Physics Mechanics
• Chemistry Chemical Reactions Chemical Properties
• Finance Simple Interest Compound Interest Present Value Future Value
• Economics Point of Diminishing Return
• Conversions Roman Numerals Radical to Exponent Exponent to Radical To Fraction To Decimal To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians Hexadecimal Scientific Notation Distance Weight Time Volume
• Pre Algebra
• Pre Calculus
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• arithmetic\:mean\:1,\:2,\:3,\:4,\:5,\:6
• geometric\:mean\:\left\{0.42,\:0.52,\:0.58,\:0.62\right\}
• quadratic\:mean\:-4,\:5,\:6,\:9
• median\:\:\left\{1,\:7,\:-3,\:4,\:9\right\}
• mode\:\left\{90,\:94,\:53,\:68,\:79,\:94,\:87,\:90,\:70,\:69,\:65,\:89,\:85\right\}
• minimum\:-4,\:5,\:6,\:9
• maximum\:\frac{31}{100},\:\frac{23}{105},\:\frac{31}{205},\:\frac{54}{205}
• mid\:range\:1,\:2,\:3,\:4,\:5,\:6
• range\:\:\left\{1,\:7,\:-3,\:4,\:9\right\}
• standard\:deviation\:\:\left\{1,\:7,\:-3,\:4,\:9\right\}
• variance\:1,\:2,\:3,\:4,\:5,\:6
• lower\:quartile\:-4,\:5,\:6,\:9
• upper\:quartile\:\left\{0.42,\:0.52,\:0.58,\:0.62\right\}
• interquartile\:range\:1,\:2,\:3,\:4,\:5,\:6
• midhinge\:\left\{90,\:94,\:53,\:68,\:79,\:84,\:87,\:72,\:70,\:69,\:65,\:89,\:85\right\}
• What is the best calculator for statistics?
• Symbolab offers an online calculator specifically for statistics that can perform a wide range of calculations, including standard deviation, variance, range and normal distribution. It also provides detailed step-by-step solutions.
• What is statistics?
• Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. There are two main branches of statistics: descriptive statistics, and inferential statistics.
• What is descriptive statistics?
• Descriptive statistics is a branch of statistics that deals with summarizing, organizing and describing data. Descriptive statistics uses measures such as central tendency (mean, median, and mode) and measures of variability (range, standard deviation, variance) to give an overview of the data.
• What is inferential statistics?
• Inferential statistics is a branch of statistics that deals with making predictions and inferences about a population based on a sample of data. Inferential statistics uses probability theory and statistical models to make predictions and inferences about a population.
• What is the difference between statistics and probability?
• Statistics is the branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data, while probability is the branch of mathematics dealing with the likelihood of occurrence of different events.

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• Lies, Damned Lies, and Statistics Statistics is about analyzing data, for instance the mean is commonly used to measure the “central tendency” of...

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11 Surprising Homework Statistics, Facts & Data

The age-old question of whether homework is good or bad for students is unanswerable because there are so many “ it depends ” factors.

For example, it depends on the age of the child, the type of homework being assigned, and even the child’s needs.

There are also many conflicting reports on whether homework is good or bad. This is a topic that largely relies on data interpretation for the researcher to come to their conclusions.

To cut through some of the fog, below I’ve outlined some great homework statistics that can help us understand the effects of homework on children.

Homework Statistics List

1. 45% of parents think homework is too easy for their children.

A study by the Center for American Progress found that parents are almost twice as likely to believe their children’s homework is too easy than to disagree with that statement.

Here are the figures for math homework:

• 46% of parents think their child’s math homework is too easy.
• 25% of parents think their child’s math homework is not too easy.
• 29% of parents offered no opinion.

Here are the figures for language arts homework:

• 44% of parents think their child’s language arts homework is too easy.
• 28% of parents think their child’s language arts homework is not too easy.
• 28% of parents offered no opinion.

These findings are based on online surveys of 372 parents of school-aged children conducted in 2018.

2. 93% of Fourth Grade Children Worldwide are Assigned Homework

The prestigious worldwide math assessment Trends in International Maths and Science Study (TIMSS) took a survey of worldwide homework trends in 2007. Their study concluded that 93% of fourth-grade children are regularly assigned homework, while just 7% never or rarely have homework assigned.

3. 17% of Teens Regularly Miss Homework due to Lack of High-Speed Internet Access

A 2018 Pew Research poll of 743 US teens found that 17%, or almost 2 in every 5 students, regularly struggled to complete homework because they didn’t have reliable access to the internet.

This figure rose to 25% of Black American teens and 24% of teens whose families have an income of less than $30,000 per year.

4. Parents Spend 6.7 Hours Per Week on their Children’s Homework

A 2018 study of 27,500 parents around the world found that the average amount of time parents spend on homework with their child is 6.7 hours per week. Furthermore, 25% of parents spend more than 7 hours per week on their child’s homework.

American parents spend slightly below average at 6.2 hours per week, while Indian parents spend 12 hours per week and Japanese parents spend 2.6 hours per week.

5. Students in High-Performing High Schools Spend on Average 3.1 Hours per night Doing Homework

A study by Galloway, Conner & Pope (2013) conducted a sample of 4,317 students from 10 high-performing high schools in upper-middle-class California. 

Across these high-performing schools, students self-reported that they did 3.1 hours per night of homework.

Graduates from those schools also ended up going on to college 93% of the time.

6. One to Two Hours is the Optimal Duration for Homework

A 2012 peer-reviewed study in the High School Journal found that students who conducted between one and two hours achieved higher results in tests than any other group.

However, the authors were quick to highlight that this “t is an oversimplification of a much more complex problem.” I’m inclined to agree. The greater variable is likely the quality of the homework than time spent on it.

Nevertheless, one result was unequivocal: that some homework is better than none at all : “students who complete any amount of homework earn higher test scores than their peers who do not complete homework.”

7. 74% of Teens cite Homework as a Source of Stress

A study by the Better Sleep Council found that homework is a source of stress for 74% of students. Only school grades, at 75%, rated higher in the study.

That figure rises for girls, with 80% of girls citing homework as a source of stress.

Similarly, the study by Galloway, Conner & Pope (2013) found that 56% of students cite homework as a “primary stressor” in their lives.

8. US Teens Spend more than 15 Hours per Week on Homework

The same study by the Better Sleep Council also found that US teens spend over 2 hours per school night on homework, and overall this added up to over 15 hours per week.

Surprisingly, 4% of US teens say they do more than 6 hours of homework per night. That’s almost as much homework as there are hours in the school day.

The only activity that teens self-reported as doing more than homework was engaging in electronics, which included using phones, playing video games, and watching TV.

9. The 10-Minute Rule

The National Education Association (USA) endorses the concept of doing 10 minutes of homework per night per grade.

For example, if you are in 3rd grade, you should do 30 minutes of homework per night. If you are in 4th grade, you should do 40 minutes of homework per night.

However, this ‘rule’ appears not to be based in sound research. Nevertheless, it is true that homework benefits (no matter the quality of the homework) will likely wane after 2 hours (120 minutes) per night, which would be the NEA guidelines’ peak in grade 12.

10. 21.9% of Parents are Too Busy for their Children’s Homework

An online poll of nearly 300 parents found that 21.9% are too busy to review their children’s homework. On top of this, 31.6% of parents do not look at their children’s homework because their children do not want their help. For these parents, their children’s unwillingness to accept their support is a key source of frustration.

11. 46.5% of Parents find Homework too Hard

The same online poll of parents of children from grades 1 to 12 also found that many parents struggle to help their children with homework because parents find it confusing themselves. Unfortunately, the study did not ask the age of the students so more data is required here to get a full picture of the issue.

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Interpreting the Data

Unfortunately, homework is one of those topics that can be interpreted by different people pursuing differing agendas. All studies of homework have a wide range of variables, such as:

• What age were the children in the study?
• What was the homework they were assigned?
• What tools were available to them?
• What were the cultural attitudes to homework and how did they impact the study?
• Is the study replicable?

The more questions we ask about the data, the more we realize that it’s hard to come to firm conclusions about the pros and cons of homework .

Furthermore, questions about the opportunity cost of homework remain. Even if homework is good for children’s test scores, is it worthwhile if the children consequently do less exercise or experience more stress?

Thus, this ends up becoming a largely qualitative exercise. If parents and teachers zoom in on an individual child’s needs, they’ll be able to more effectively understand how much homework a child needs as well as the type of homework they should be assigned.

Related: Funny Homework Excuses

The debate over whether homework should be banned will not be resolved with these homework statistics. But, these facts and figures can help you to pursue a position in a school debate on the topic – and with that, I hope your debate goes well and you develop some great debating skills!

Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 5 Top Tips for Succeeding at University
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• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 100 Consumer Goods Examples
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 30 Globalization Pros and Cons

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Homework help

Necessity of online homework help.

Contemporary world is a scene for competitions. Starting at early childhood environment immerse us into struggle for best positions. With constant population growth it becomes harder to get a place in kindergartens, schools for gifted children, prestigious universities and, of course, you are not alone in desire to have a well-paid job. Children since early age know that they must study hard, devote themselves into different subjects, and be successful and active in post-school projects. Under pressure of numerous complex tasks no wonder they often require homework help. For their needs special websites were launched. And now every child can get guidance and online homework help from every corner of the world. With opportunity to ask questions about necessary subjects he will at his own pace learn information. This also adds more individuality to process of studying, as children might experience problems with concentrated and fast group-learning. Online homework help is not merely a way to make grades better and to finish all tasks in time, it's personal attention and support. Websites offer plenty of subjects to work at, but according to searches most popular (as it's complicated to understand) is math homework help. This subject is a nightmare for both schoolchildren and their parents.

Why using college homework help is beneficial

It might come as surprise for graduates but when you enter college or university, amount of homework will be only increasing. Yes, besides lectures and practical courses you are obliged to do some homework too. And it might be incredibly more complicated than all things you have done in school. Plenty of students are struggling to cope with amount of tasks themselves but some are looking for websites for college homework help. With current subjects, with unknown teachers, with new classrooms it's stressful enough for young people to be focused. That's why students choose homework help discord, a place to discuss all difficulties online and solve problems. With guidance and support of experts it's easier to understand unknown topics and work on self-improvement. It's recommended not to torture yourself and get accounting homework help or any other kind of assistance. With wide range of professionals you can find a person no matter how complicated your task is.

Is it safe to trust strangers with important tasks?

Looking for online help with college or school tasks you might doubt reliability of person who is assisting you from other side of screen. How is it possible to find a proper tutor for difficult statistics homework help? Read reviews, study information, ask for certificates or diplomas to be assured you hire a true expert to perform job