CONFIDENTIAL 1

Grade 8 Algebra1Grade 8 Algebra1

Frequency andFrequency andHistogramsHistograms

CONFIDENTIAL 2

Warm UpWarm Up

Use the circle graph for Exercises 1–3.

1) Which two types of gifts make up just over half of the donated gifts?

2) Which type of gift represents 1/5 of the total donated gifts?

3) If there were 160 gifts donated, how many were books?

CONFIDENTIAL 3

A stem-and-leaf plot arranges data by dividing each data value into two parts. This allows you to see each data value.

Frequency and HistogramsFrequency and Histograms

Stem-and-leaf plots can be used to organize data, like the number of students in elective classes.

The last digit of a value is called

a leaf.The digits other

than the last digit of each value are

called a stem.

2 3

The key tells you how to read each

value.Key: 2|3 means 23

CONFIDENTIAL 4

Making a Stem-and-Leaf PlotMaking a Stem-and-Leaf Plot

A) The numbers of students in each of the elective classes at a school are given below. Use the data to make a stem-and-leaf plot.

24, 14, 12, 25, 32, 18, 23, 24, 9, 18, 34, 28, 24, 27.

Key: 2|3 means 23

The tens digits are the stems.

The ones digits are the leaves.

List the leaves from least to greatest within each row.

Title the graph and add a key.

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B) Marty’s and Bill’s scores for ten games of bowling are given below. Use the data to make a back-to-back stem-and-leaf plot.

Marty: 137, 149, 167, 134, 121, 127, 143, 123, 168, 162Bill: 129, 138, 141, 124, 139, 160, 149, 145, 128, 130

The first two digits are the stems.

The ones digits are the leaves.

Put Marty’s scores on the left side and Bill’s scores on the right.

Title the graph and add a key.

The graph shows that three of Marty’s scores were higher than Bill’s highest score.

Key: |14|1 means 141Key: 3|14| means 143

CONFIDENTIAL 6

Now you try!

1) The temperature in degrees Celsius for two weeks are given below. Use the data to make a stem-and-leaf plot.

7, 32, 34, 31, 26, 27, 23, 19, 22, 29, 30, 36, 35, 31

CONFIDENTIAL 7

The frequency of a data value is the number of times it occurs. A frequencytable shows the frequency of each data

value. If the data is divided intointervals, the table shows the frequency of

each interval.

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Making a Frequency TableMaking a Frequency Table

The final scores for each golfer in a tournament are given below. Use the data to make a frequency table with intervals.

77, 71, 70, 82, 75, 76, 72, 70, 77, 74, 71, 75, 68, 72, 75, 74

Step3 List the intervals in the firstcolumn of the table. Count the number of data values in each interval and list the count in the last column. Give the table a title.

Step1 Identify the least and greatest values.The least value is 68. The greatest value is 82.

Step2 Divide the data into equal intervals.For this data set, use an interval of 3.

CONFIDENTIAL 9

Now you try!

2) The number of days of Maria’s last 15 vacations are listed below. Use the data to make a frequency table

with intervals.

4, 8, 6, 7, 5, 4, 10, 6, 7, 14, 12, 8, 10, 15, 12

CONFIDENTIAL 10

A histogram is a bar graph used to display the frequency of data divided

into equal intervals. The bars must be of equal width and should touch,

but not overlap.

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Making a HistogramMaking a Histogram

Use the following frequency table to make a histogram.

Step1 Use the scale and interval from the frequency table.

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Step2 Draw a bar for the number of scores in each interval.All bars should be the same width. The bars should touch, but not overlap.

Step3 Title the graph and label the horizontal and vertical scales.

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Now you try!

3) Make a histogram for the number of days of Maria’s last15 vacations.

4, 8, 6, 7, 5, 4, 10, 6, 7, 14, 12, 8, 10, 15, 12

CONFIDENTIAL 14

Cumulative frequency shows the frequency of all data values less than or

equal to a given value. You could just count the number of values, but if the data

set has many values, you might lose track. Recording the data in a cumulative

frequency table can help you keep track of the data values as you count.

CONFIDENTIAL 15

Making a Cumulative Frequency TableMaking a Cumulative Frequency Table

The heights in inches of the players on a school basketball teamare given below.

72, 68, 71, 70, 73, 69, 79, 76, 72, 75, 72, 74, 68, 70, 69, 75, 72, 71, 73, 76

a) Use the data to make a cumulative frequency table.

Step1 Choose intervals for the first column of the table.

Step2 Record the frequency of values in each interval for the second column.

Step3 Add the frequency of each interval to the frequencies of all the intervals before it. Put that number in the third column of the table.

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Step4 Title the table.

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b) How many players have heights under 74 in?

All heights under 74 in. are displayed in the first two rows of the table, so look at the cumulative frequency shown

in the second row.There are 14 players with heights under 74 in.

CONFIDENTIAL 18

Now you try!

4) The number of vowels in each sentence of a short essay are listed below.

33, 36, 39, 37, 34, 35, 43, 35, 28, 32, 36, 35, 29, 40, 33, 41, 37

a. Use the data to make a cumulative frequency table.b. How many sentences contain 35 vowels or fewer?

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Assessment

1 )The ages of professional basketball players at the time the players were recruited are given below. Use the data to

make a stem-and-leaf plot.

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2) The average monthly rainfall for two cities (in inches) is given below. Use the data to make a back-to-back

stem-and-leaf plot.

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3) The finishing times of runners in a 5K race, to the nearest minute, are given below. Use the data to make

a frequency table with intervals.

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4) The breathing intervals of gray whales are given. Use the frequency table to make a histogram for the data.

CONFIDENTIAL 23

5) The scores made by a group of eleventh-grade studentson the mathematics portion of the SAT are given.

a. Use the data to make a cumulative frequency table.

b. How many students scored 650 or higher on the mathematics portion of the SAT?

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6) The numbers of people who visited a park each day over two weeks during different seasons are given below. Use the data to make a back-to-back stem-and-leaf plot.

CONFIDENTIAL 25

A stem-and-leaf plot arranges data by dividing each data value into two parts. This allows you to see each data value.

Frequency and HistogramsFrequency and Histograms

Stem-and-leaf plots can be used to organize data, like the number of students in elective classes.

The last digit of a value is called

a leaf.

The digits other than the last digit of each value are

called a stem.

2 3

The key tells you how to read each

value.Key: 2|3 means 23

Let’s review

CONFIDENTIAL 26

Making a Stem-and-Leaf PlotMaking a Stem-and-Leaf Plot

A) The numbers of students in each of the elective classes at a school are given below. Use the data to make a stem-and-leaf plot.

24, 14, 12, 25, 32, 18, 23, 24, 9, 18, 34, 28, 24, 27.

Key: 2|3 means 23

The tens digits are the stems.

The ones digits are the leaves.

List the leaves from least to greatest within each row.

Title the graph and add a key.

CONFIDENTIAL 27

B) Marty’s and Bill’s scores for ten games of bowling are given below. Use the data to make a back-to-back stem-and-leaf plot.

Marty: 137, 149, 167, 134, 121, 127, 143, 123, 168, 162Bill: 129, 138, 141, 124, 139, 160, 149, 145, 128, 130

The first two digits are the stems.

The ones digits are the leaves.

Put Marty’s scores on the left side and Bill’s scores on the right.

Title the graph and add a key.

The graph shows that three of Marty’s scores were higher than Bill’s highest score.

Key: |14|1 means 141Key: 3|14| means 143

CONFIDENTIAL 28

Making a Frequency TableMaking a Frequency Table

The final scores for each golfer in a tournament are given below. Use the data to make a frequency table with intervals.

77, 71, 70, 82, 75, 76, 72, 70, 77, 74, 71, 75, 68, 72, 75, 74

Step3 List the intervals in the firstcolumn of the table. Count the number of data values in each interval and list the count in the last column. Give the table a title.

Step1 Identify the least and greatest values.The least value is 68. The greatest value is 82.

Step2 Divide the data into equal intervals.For this data set, use an interval of 3.

CONFIDENTIAL 29

Making a HistogramMaking a Histogram

Use the following frequency table to make a histogram.

Step1 Use the scale and interval from the frequency table.

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Step2 Draw a bar for the number of scores in each interval.All bars should be the same width. The bars should touch, but not overlap.

Step3 Title the graph and label the horizontal and vertical scales.

CONFIDENTIAL 31

You did a great job You did a great job today!today!