data representation and interpretation grade 11

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DATA REPRESENTATION AND PREDICTION (Daththa Nirupanaya Ha Arthakathanaya) | Grade 11 Maths Textbook Answers

Grade 11 Maths Textbook Answers Lesson 15 - DATA REPRESENTATION AND PREDICTION (Daththa Nirupanaya Ha Arthakathanaya)

Download Grade 11 Maths textbook answers for DATA REPRESENTATION AND PREDICTION (Daththa Nirupanaya Ha Arthakathanaya), Lesson 15 in Sinhala Medium. DATA REPRESENTATION AND PREDICTION (Daththa Nirupanaya Ha Arthakathanaya) Answers are available in PDF format. Download using the Link Below. It’s free to download.

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Represent and interpret data

Here you will learn how to represent and interpret data, including how to show categorical and discrete data with tally charts, pictographs and bar graphs.

Students will first learn how to represent and interpret data as part of measurement and data in 1 st grade and continue to grow in their skills through elementary school.

What does it mean to represent and interpret data?

To represent and interpret data , first collect data and then show it visually – in a table or on a graph. This is representing data. Interpreting data is using data analysis to answer questions.

One easy way to collect and represent data is with a tally chart . To do this, sort the data into categories and use tally marks to show the frequencies.

For example,

A benefit of the tally chart is that it is very clear which category occurs the most or least frequently, and can be helpful when analyzing data.

• Which color is most popular? Green ← This can be clearly seen by the amount of tally marks

*Note: Tally charts can be useful both during data collection and data analysis.

Step-by-step guide: Tally Chart

A pictograph or a picture graph uses pictures to show data.

To draw a pictograph, you use a symbol to represent the frequency. The key of the pictograph shows the value of the symbol.

A benefit of the pictograph is that it is very clear which category occurs the most or least frequently, and can be helpful when analyzing data.

What is the most popular sport among the students? Tennis ← This can be clearly seen by the amount of smiley faces

Pictographs are different from tally marks, in that pictographs do not always show the exact number.

• How many students play golf? 4 ← Even though there are only 2 smiley faces, each smiley face is 2 students, so the total is 4

Step-by-step guide: Pictograph

A bar graph shows a data set by using vertical or horizontal bars. The longer the bar, the higher the value for the individual category.

To draw a bar graph:

• Draw a pair of axes. Usually the horizontal axis is labeled with the categories of the data set and the vertical axis is the frequency.
• The frequencies need to be labeled on the vertical axis in equal intervals.
• The bars need to have equal gaps between them.
• The bars need to be of equal width.
• The chart needs a title.

Step-by-step guide: Bar Graph

What is represent and interpret data

[FREE] Represent and Interpret Data Worksheet (Grade 1 to 3)

Use this quiz to check your 1st, 2nd and 3rd grade students’ understanding of representing and interpreting data. 15+ questions with answers covering a range of 1st, 2nd and 3rd grade represent and interpret data topics to identify learning gaps!

Common Core State Standards

How does this relate to elementary school math?

• Grade 1: Measurement and Data (1.MD.C.4) Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.
• Grade 2: Operations and algebraic thinking (2.OA.C.3) Determine whether a group of objects ( up to 20) has an odd or even number of members, example, by pairing objects or counting them by 2 s; write an equation to express an even number as a sum of two equal addends.
• Grade 3 – Measurement and Data (3.MD.B.3) Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs.
• Grade 4 – Number and Operations – Fractions (4.NF.B.3.b) Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, example, by using a visual fraction model.
• Grade 5 – Number and Operations – Base Ten (5.NBT.A.2) Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10.

How to represent and interpret data

There are a lot of ways to represent and interpret data. For more specific step-by-step guides, check out the pages linked in the “What does it mean to represent and interpret data?” section above or read through the examples below.

Represent and interpret data examples

Example 1: favorite school subject.

Below is a list of the favorite school subjects for students in class 2 a.

math, science, english, english, social studies, science, social studies, math, science, social studies, social studies, english, science, english, social studies, math, science, science, english, social studies, social studies, english, science, math, social studies, math, science, science, english.

Draw a tally chart to display this information.

• Draw a data table with \bf{3} columns.

Here you are looking at modes of transport, so the title of the first column is ‘Subject’, then you have our ‘Tally’ column, and then the ‘Frequency’ column:

2 Write the category names into each row of the table.

The data can be divided into four categories: math, science, social studies, english.

These are the labels for each row.

3 Record the data into the table using five-bar gate tally marks.

Tally each value in the data one at a time.

The final tally chart should look like:

4 Work out the frequency for each category by counting the tally marks.

Remember that a five-bar gate represents 5 tally marks.

Example 2: tally chart word problems

The tally chart below shows the favorite pet of first grade students in Ms. Ortega’s class.

(a) How many students were asked about their favorite pet?

(b) How many more students wanted a cat as a pet than a bird?

Read the question(s).

Use the information in the tally chart to answer the question(s).

To find the total number of students asked about their favorite pet, you will add up the frequency of each category.

21 students were asked about their favorite pet.

To find how many more students want a cat as a pet than a bird, you will subtract the frequencies.

3 more students wanted a cat as a pet than a bird.

Example 3: read/interpret pictograph

The pictograph below shows the number of cars sold over the course of 7 days. How many cars were sold on Day 4?

Read the key in order to find the value of each symbol.

Each car symbol represents 3 cars.

Interpret the data to answer the question.

On the pictograph, Day 4 has 5 cars.

You can skip count starting with 3.

You can add,

3+3+3+3+3=15

There were 15 cars sold on Day 4.

Example 4: construct a pictograph with graphic symbol equal to 1 unit

Use the information in the following table to construct a pictogram of the number of servings of fruit eaten each day over 5 days.

Make sure the table has the correct number of rows.

There are 5 days on the tally chart, so there should be 5 rows on the pictograph.

Label the table.

Make a key.

Count the number of graphic symbols needed in each row.

Since the key is 1, the number of apples will be the same as the total fruit servings.

Place the graphic symbols into the pictograph.

Example 5: constructing a standard bar graph

Draw a bar graph to represent the favorite dessert of students.

Draw the axes with a ruler and label them.

Use a ruler to draw each bar with the correct height.

There are 5 in the first category, so draw a bar with the height of 5 units on the vertical axis. Repeating this for each category, you get the bar graph:

Give the chart a title.

Example 6: solving problems from a bar graph

Mr. Li’s class voted on which activity was their favorite to play at recess. The bar graph below represents the results.

How many more students voted for tag than soccer?

Locate the necessary bar(s).

The two bars that you need to locate are tag and soccer.

Read the frequency from the vertical axis.

The frequency is read from the top of the bar.

7 students voted for tag as their favorite activity.

4 students voted for soccer as their favorite activity.

Complete the calculation.

To calculate how many more students voted for tag than soccer, you will subtract the two quantities.

3 more students voted for tag than soccer as their favorite recess activity.

Teaching tips to represent and interpret data

• Use back to school math activities to introduce students to each other and data in a fun way that involves problem solving. Ask each student to collect data about their new classmates – what is their favorite food, how many siblings do they have, how many books did they read over the summer, etc. Then have students represent their collected data with a tally chart, pictograph or bar graph. Lastly students can create questions that prompt their classmates to interpret the data.
• Instead of just using math printable worksheets to teach students how to collect, represent and interpret data, utilize interactive online resources and apps in your lesson plans to make learning fun and engaging.

Easy mistakes to make

• Confusing the total frequency and the number of categories The number of categories is not the same as the total frequency. Be careful when asked for the total number. This means the total frequency NOT the number of categories. For example, In example 1, there are 4 different school subjects – this is not the total frequency. The total frequency was the total number of students represented by the data.
• Forgetting to group tally marks in fives A fifth tally line should always be drawn through the previous four tally marks, creating a five bar gate. For example, To represent 8\text{:} ➜ Correct: |||| ||| ➜ Incorrect: ||||||||

• Not leaving space between bars in a bar graph It’s important to leave space between the bars so that it is clear that each bar represents a different group. This also makes the data easier to read and ensures that the bar graph does not look like a histogram.
• Not labeling an axis The horizontal and vertical axes need to have labels to name what they represent. This allows you to correctly use and interpret the data given.

Practice represent and interpret data questions

1. A children’s shoe shop took a survey of types of shoes sold over one day. Here is a list of their responses.

boots \hspace{0.7cm} sneakers \hspace{0.35cm} sneakers \hspace{0.35cm} sneakers \hspace{0.5cm} sandals \hspace{0.5cm} boots

sandals \hspace{0.45cm} boots \hspace{0.8cm} boots \hspace{0.75cm} sandals \hspace{0.65cm} sneakers \hspace{0.35cm} sneakers

sneakers \hspace{0.3cm} sandals \hspace{0.5cm} sandals \hspace{0.5cm} sneakers \hspace{0.5cm} boots \hspace{0.8cm} boots

Select the correct tally chart that represents the information above.

After counting the data points, the shoe store sold 5 pairs of sandals, 7 pairs of sneakers and 6 pairs of boots, which only leaves two answer choices:

Five-bar gate notation should be used, which leaves only one correct tally chart:

2. The tally chart below shows the favorite season of students in a class.

How many students does the data represent?

25 students

28 students

14 students

To find the number of students, you will add the frequency:

The data represents 28 students.

3. Some 2 nd grade and 3 rd grade students were asked what their favorite pizza place was. The pictograph below shows their responses.

If 32 students like Pizza Parlour, how many like Mama Joan’s?

38 students

44 students

22 students

Pizza Parlor has 2 circles, with a total of 16 slices. Since 16 \times 2=32 students, that means each slice represents 2 students.

Mama Joan’s has 22 slices and 22 \times 2=44 students.

4. A pre-k program records the number of children that attend their after school program in a week. The pictogram below shows their results.

How many more children attended on Thursday than Friday?

Now we can use these values to find the totals for Thursday and Friday.

To find the difference, use subtraction:

4 more children attended on Friday than Thursday.

5. The graph below shows the number of students who attend an elementary school, middle school and a high school.

How many more students attend the middle school than the high school?

40 students

20 students

Each line in the grid represents 10, so the graph is counting up by 10 s.

This means the total for middle school is 180 and the total for high school is 140.

180-140=40, so middle school is 40 more than high school.

6. Draw a bar graph to represent the favorite book genres of students.

Bar graphs do not have to be in the same order as they are listed on the table. However, they do have to have the same values from the table.

The graph below matches the data from the table.

Represent and interpret data FAQs

A frequency table shows the total of a group within a data set. Students begin to explore frequency tables in elementary school and continue advancing in complexity through middle school and high school.

Line plots are a way to represent numerical data – as they use a number line to plot data. Students begin exploring line plots in elementary school. Step-by-step guide : Line plot

Pie charts are a way to represent data out of a whole. Specifically a whole represented by 100\%. The area of the circle that a data category takes up is proportional to its percentage of the data. Students explore pie charts in middle school.

The next lessons are

• Converting fractions, decimals, and percentages

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Digital SAT Math

Course: digital sat math   >   unit 3, data representations | lesson.

• Key features of graphs — Basic example
• Key features of graphs — Harder example
• Data representations: foundations

What are data representations problems?

• Read types of graphs that commonly appear on the SAT
• Create line graphs based on verbal descriptions

How do I read bar graphs, dot plots, and histograms?

Reading bar graphs, what are bar graphs, dot plots, and histograms.

• Since cereals brands C and D have taller bars than cereal brands A and B, we can immediately tell that cereal brands C and D have more sugar per 100 ‍   grams of cereal than cereal brands A and B.
• Cereal brands A and B have close to 10 ‍   grams of sugar per 100 ‍   grams of cereal, while cereal brands C and D have over 30 ‍   grams of sugar per 100 ‍   grams of cereal.
• This means cereal brands C and D have over triple the amount of sugar per 100 ‍   grams of cereal than cereal brands A and B!
• We can interpret the data as " 250 ‍   students take Spanish", "approximately 60 ‍   students take French", etc.
• Based on the relative size of the bars, we can tell that Spanish is the most frequently taken foreign language and Latin is the least frequently taken foreign language.
• 3 ‍   students take 5 ‍   minutes to travel to school, 4 ‍   students take 10 ‍   minutes to travel to school, etc.
• The most common travel time is 10 ‍   minutes.
• The travel times range from 5 ‍   to 35 ‍   minutes.
• 6 ‍   available apartments have areas between 30 ‍   and 40 ‍   square meters, 4 ‍   have areas between 40 ‍   and 50 ‍   square meters, etc.
• There aren't many larger apartments available.
• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

How do I read line graphs?

Reading line graphs, what are line graphs.

• Identify values on the graph and use them in calculations
• Determine whether the graph is increasing or decreasing. We may be asked about a specific interval or the whole graph.
• Determine when the rate of change is the highest/lowest. Higher rates of change correspond to steeper sections of the graph, and lower rates of change correspond to shallower sections of the graph.
• The voter turnout in 1992 ‍   is approximately 105 ‍   million people.
• The difference in voter turnout between 1988 ‍   and 2004 ‍   is approximately 30 ‍   million people.
• From 1980 ‍   to 2004 ‍   , voter turnout generally increased.
• However, voter turnout decreased between 1984 ‍   and 1988 ‍   and between 1992 ‍   and 1996 ‍   .
• The greatest change in voter turnout between consecutive elections occurred between 2000 ‍   and 2004 ‍   .
• The smallest change in voter turnout between consecutive elections occurred between 1984 ‍   and 1988 ‍   .

How do I draw line graphs based on verbal descriptions?

Translating a sequence of events to a line graph, what are some key phrases to look out for.

Let's look at an example!

• (Choice A)   Between the 101 ‍   st and 102 ‍   nd A Between the 101 ‍   st and 102 ‍   nd
• (Choice B)   Between the 102 ‍   nd and 103 ‍   rd B Between the 102 ‍   nd and 103 ‍   rd
• (Choice C)   Between the 103 ‍   rd and 104 ‍   th C Between the 103 ‍   rd and 104 ‍   th
• (Choice D)   Between the 104 ‍   th and 105 ‍   th D Between the 104 ‍   th and 105 ‍   th
• a proper fraction, like 1 / 2 ‍   or 6 / 10 ‍  
• an improper fraction, like 10 / 7 ‍   or 14 / 8 ‍  
• (Choice A)   A
• (Choice B)   B
• (Choice C)   C
• (Choice D)   D

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Free Printable data visualization Worksheets for 11th Grade

Math data visualization made accessible! Discover a collection of free printable worksheets for Grade 11 students, designed to enhance their understanding of complex mathematical concepts through visually appealing representations. Empower your teaching with Quizizz!

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Data visualization worksheets for Grade 11 are an essential resource for teachers looking to enhance their students' understanding of Math, probability, and statistics. These worksheets provide a visual representation of complex data sets, allowing students to easily comprehend and analyze the information presented. By incorporating these worksheets into their lesson plans, teachers can effectively engage their students and help them develop critical thinking skills. Additionally, these worksheets can be used to reinforce concepts taught in class, providing students with ample opportunities to practice and improve their skills. With a variety of topics covered, such as bar graphs, pie charts, and scatter plots, data visualization worksheets for Grade 11 are an invaluable tool for any teacher looking to elevate their Math, probability, and statistics curriculum.

Quizizz is an excellent platform for teachers to access data visualization worksheets for Grade 11, along with a plethora of other resources. This interactive platform offers a wide range of quizzes, games, and activities that can be easily integrated into lesson plans, making learning Math, probability, and statistics more engaging and enjoyable for students. Teachers can also create their own quizzes and worksheets, tailoring the content to suit their students' needs and learning objectives. Furthermore, Quizizz provides real-time feedback and analytics, allowing teachers to monitor their students' progress and identify areas that may require additional support or instruction. By utilizing Quizizz in conjunction with data visualization worksheets for Grade 11, teachers can create a comprehensive and dynamic learning experience that will undoubtedly benefit their students.

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Data Representation and Interpretation Worksheets - Foundation

Updated:  12 Jun 2020

2 data representation and location worksheets linked to the Australian Curriculum.

Non-Editable:  PDF

Pages:  4 Pages

• Curriculum Curriculum:  AUS V8, NSW, VIC, AUS V9
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This teaching resource  could be used in a variety of ways when teaching data representation and interpretation . Some suggestions include:

• pre- and post-testing
• independent classwork
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This teaching resource pack includes worksheets addressing the following concepts:

• data representation and interpretation.

Answer sheets are also provided.

Download options include:

• the year level displayed at the top of the sheet
• no year level displayed at the top of the sheet to use for differentiation.

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