Frequency Tables, Line Plots, and Histograms

Frequency Tables, Line Plots, and HistogramsFrequency Tables, Line Plots, and HistogramsPRE-ALGEBRA LESSON 12-1PRE-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

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PRE-ALGEBRA LESSON 12-1PRE-ALGEBRA LESSON 12-1

Solutions

1. 5, 6, 9, 9, 9 2. 73, 73, 77, 78, 79median = 9 median = 77mode = 9 mode = 73

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

Frequency Tables, Line Plots, and HistogramsFrequency Tables, Line Plots, and Histograms

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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 32 2 1 3 2 1 2 3 2 4 3

Number Tally Frequency

List the numbers of hours in order.

1

2

3

4

Count the tally marks andrecord the frequency.

3

7

6

6

Use a tally mark for each result.

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Quick Check

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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.


“How many cases are you trying?”

Number Frequency 0 3 1 5 2 4 3 5 4 4


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(continued)


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

For a line plot, follow these steps 1 , 2 , and 3 .

3 Write a title that describes the data.Cases Tried by Judges

2 Mark an x for each response.

x xx x x x

x x x x xx x x x xx x x x x

1 Draw a number line with the choices below it.

0 1 2 3 4


Quick Check

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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.

Pets Tally Frequency0 IIII 51 IIII II 72 III 33 II 2

range: 12


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Box-and-Whisker PlotsBox-and-Whisker PlotsPRE-ALGEBRA LESSON 12-2PRE-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

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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

9 + 102

4.8 + 52

52 + 522

101 + 1012

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Box-and-Whisker PlotsBox-and-Whisker Plots

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 35 40 49 54 61 61 62 72 75lower quartile = 28upper quartile = 61

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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.


(continued)

Quick Check

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Draw a number line for both sets of data. Use the range of data points to choose a scale.

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


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

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


The lowest score is 55 and the highest is 85.

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

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

Quick Check

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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

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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.

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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.

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Documents

Frequency Tables, Line Plots, and Histograms