Frequency Tables, Line Plots, and Histograms

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Frequency Tables, Line Plots, and Histograms. PRE-ALGEBRA LESSON 12-1. (For help, go to Lesson 3-3.). Find the median and mode of each data set. 1. 6, 9, 9, 5, 9 2. 73, 78, 77, 73, 79 3. 300, 100, 200, 150, 300 4. 3, 5, 7, 9, 3, 4, 6, 3, 7. Check Skills You’ll Need. 12-1.

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Frequency Tables, Line Plots, and Histograms

PRE-ALGEBRA LESSON 12-1

(For help, go to Lesson 3-3.)

Find the median and mode of each data set.

1. 6, 9, 9, 5, 9 2. 73, 78, 77, 73, 79

3. 300, 100, 200, 150, 300 4. 3, 5, 7, 9, 3, 4, 6, 3, 7

Check Skills You’ll Need

12-1

Frequency Tables, Line Plots, and Histograms

PRE-ALGEBRA LESSON 12-1

Solutions

1. 5, 6, 9, 9, 9 2. 73, 73, 77, 78, 79

median = 9 median = 77

mode = 9 mode = 73

3. 100, 150, 200, 300, 300 4. 3, 3, 3, 4, 5, 6, 7, 7, 9

median = 200 median = 5

mode = 300 mode = 3

12-1

List the numbers of

hours in order.

Use a tally mark

for each result.

Count the tally marks and

record the frequency.

Number

Tally

Frequency

1

6

|||| |

6

2

|||| |

3

7

|||| ||

4

|||

3

Frequency Tables, Line Plots, and Histograms

PRE-ALGEBRA LESSON 12-1

Quick Check

A survey asked 22 students how many hours of TV they watched daily. The results are shown. Display the data in a frequency table.

1 3 4 3 1 1 2 3 4 1 3

2 2 1 3 2 1 2 3 2 4 3

12-1

“How many cases are you trying?”

Number Frequency

0 3

1 5

2 4

3 5

4 4

Frequency Tables, Line Plots, and Histograms

PRE-ALGEBRA LESSON 12-1

Twenty-one judges were asked how many cases they were trying on Monday. The frequency table below shows their responses. Display the data in a line plot. Then find the range.

12-1

3 Write a title that describes the data.

Cases Tried by Judges

x x

x x x x

x x x x x

x x x x x

x x x x x

2 Mark an x for each

response.

0 1 2 3 4

1 Draw a number line with the choices below it.

Frequency Tables, Line Plots, and Histograms

PRE-ALGEBRA LESSON 12-1

(continued)

The greatest value in the data set is 4 and the least value is 0. So the range is 4 – 0, or 4.

Quick Check

12-1

Pets Tally Frequency

0 IIII 5

1 IIII II 7

2 III 3

3 II 2

range: 12

Frequency Tables, Line Plots, and Histograms

PRE-ALGEBRA LESSON 12-1

Solve.

1. Maria surveyed friends to find out how

many pets each one has.

The responses are below.

Display the data in a frequency table.

0, 1, 1, 2, 3, 0, 1, 1, 3, 2, 1, 2, 1, 0, 1, 0, 0

2. Here are the numbers of books students

read in the last month: 5, 4, 0, 12, 4, 5,

4, 3, 10, 5, 12, 3, 5, 7, 3, 10, 5, 0, 6.

Display the data in a line plot.

Then find the range.

12-1

Box-and-Whisker Plots

PRE-ALGEBRA LESSON 12-2

(For help, go to Lesson 3-3.)

Find each median.

1. 12, 10, 11, 7, 9, 8, 10, 5

2. 4.5, 3.2, 6.3, 5.2, 5, 4.8, 6, 3.9

3. 55, 53, 67, 52, 50, 49, 51, 52, 52, 52

4. 101, 100, 100, 105, 102, 101

Check Skills You’ll Need

12-2

52 + 52

2

4.8 + 5

2

9 + 10

2

101 + 101

2

Box-and-Whisker Plots

PRE-ALGEBRA LESSON 12-2

Solutions

1. 5, 7, 8, 9, 10, 10, 11, 12

median = = 9.5

2. 3.2, 3.9, 4.5, 4.8, 5, 5.2, 6, 6.3

median = = 4.9

3. 49, 50, 51, 52, 52, 52, 52, 53, 55, 67

median = = 52

4. 100, 100, 101, 101, 102, 105

median = = 101

12-2

Box-and-Whisker Plots

PRE-ALGEBRA LESSON 12-2

The data below represent the wingspans in centimeters of captured birds. Make a box-and-whisker plot.

61 35 61 22 33 29 40 62 21 49 72 75 28 21 54

Step 1 Arrange the data in order from least to greatest. Find the median.

21 21 22 28 29 33 35 40 49 54 61 61 62 72 75

Step 2  Find the lower quartile and upper quartile, which are the medians of the

lower and upper halves.

21 21 22 28 29 33 354049 54 61 61 62 72 75

lower quartile = 28

upper quartile = 61

12-2

Step 3 Draw a number line.

Mark the least and greatest values, the median, and the quartiles.

Draw a box from the first to the third quartiles.

Mark the median with a vertical segment.

Draw whiskers from the box to the least and greatest values.

Box-and-Whisker Plots

PRE-ALGEBRA LESSON 12-2

(continued)

Quick Check

12-2

points to choose a scale.

Draw the second box-and-whisker plot below the first one.

Box-and-Whisker Plots

PRE-ALGEBRA LESSON 12-2

Use box-and-whisker plots to compare test scores from two math classes.

Class A: 92, 84, 76, 68, 90, 67, 82, 71, 79, 85, 79

Class B: 78, 93, 81, 98, 69, 95, 74, 87, 81, 75, 83

Quick Check

12-2

Box-and-Whisker Plots

PRE-ALGEBRA LESSON 12-2

Describe the data in the box-and-whisker plot.

The lowest score is 55 and the highest is 85.

One fourth of the scores are at or below 66 and one fourth of the scores are at or above 80.

Half of the scores are at or between 66 and 80 and thus within 10 points of the median, 76.

Quick Check

12-2

Box-and-Whisker Plots

PRE-ALGEBRA LESSON 12-2

The plots below compare the percents of students who were eligible to those who participated in extracurricular activities in one school from 1992 to 2002. What conclusions can you draw?

About 95% of the students were eligible to participate in extracurricular activities.

Around 60% of the students did participate.

A little less than two thirds of the eligible students participated in extracurricular activities.

Quick Check

12-2

Box-and-Whisker Plots

PRE-ALGEBRA LESSON 12-2

Solve.

1. Use the data to make a box-and-whisker plot.

Student heights (in.) are: 60, 66, 59, 67, 68, 63, 62, 61, 69, 64, 61.

a. What is the median height?

b. Between what heights do 50% of the students fall?

63 in.

between 61 in. and 67 in.

12-2

Box-and-Whisker Plots

PRE-ALGEBRA LESSON 12-2

2. The box-and-whisker plots below compare prices for the same items at Mary’s Discount Store and Ed’s Clothing. What conclusions can you draw?

Prices at the discount store are more tightly grouped around the median price of \$25. Half the items cost from \$18 to \$45. For less expensive items, there is not much difference in the prices at the two stores. For more expensive items, the discount store offers lower prices.

12-2