Over Lesson 13–2

A. A

B. B

C. C

D. D

Choose the correct stem-and-leaf plot for the table.

A. B.

C. D.

3|2 = 32 stories

3|2 = 32 stories

3|2 = 32 stories

3|2 = 32 stories

You have already found measures of central tendency. (Lesson 13–2)

• Find measures of variation.

• Use measures of variation to interpret and analyze data.

• measures of variation

• range

• quartiles

• lower quartile

• upper quartile

• interquartile range

• outlier

used to describe the distribution of statistical data a measure of variation that is the difference between the least and greatest values in a data set the values that divide a set of data into four equal parts the median of the lower half of a set of data (we use “LQ” for it) the median of the upper half of a set of data (we use “UQ” for it) the range of the middle half of a set of data (UQ – LQ) data that are more than 1.5 times the interquartile range beyond the quartiles (unusual values)

Find Range

A. Find the range of the set of data.

Answer: The range is 59 – 33 or 26 hours.

3|5 = 35 hours

Stem345

Leaf3 3 5 7 7 80 3 3 4 94 9

The greatest value is 59 and the least is 33.

Work Time

Find Range

B. Find the range of the set of data.

The cost of jeans at a department store: $79, $42, $38, $51, $63, $91

The greatest value is $91 and the least is $38.

Answer: The range is $91 – $38 or $53.

A. A

B. B

C. C

D. D

A. 61

B. 65

C. 68

D. 72

A. Find the range of the set of data. {14, 37, 82, 45, 24, 10, 75}

A. A

B. B

C. C

D. D

A. 27

B. 20

C. 18

D. 12

B. Find the range of the set of data.

6|8 = 68

Stem567

Leaf2 3 5 5 94 8 90 1 8 9

Identify Measures of Variation

OLYMPICS Find the measures of variation for the data in the table.

Step 1 Range: 29 – 14 = 15 medals

Identify Measures of Variation

14 14 19 22 23 24 25 29

lower quartile median upper quartile

Interquartile range: 24.5 – 16.5 or 8

Step 2 Median, Upper Quartile, Lower Quartile

Order the data from least to greatest.

Identify Measures of Variation

Answer: The range is 15. The median is 22.5, the lower quartile is 16.5 and the upper quartile is 24.5. The interquartile range is 8.

A. A

B. B

C. C

D. D

A. R: 35, IR: 26, M: 23, LQ: 14.5, UQ: 40.5

B. R: 35, IR: 26.5, M: 24, LQ: 14, UQ: 40.5

C. R: 32, IR: 26, M: 24, LQ: 14.5, UQ: 40.5

D. R: 35, IR: 12.5, M: 23, LQ: 16, UQ: 28.5

What are the range (R), interquartile range (IR), median (M), lower quartile (LQ), and upper quartile (UQ) for the data in the table?

Find Outliers

NUTRITION Find any outliers in the data set.

Step 1 Find the interquartile range.

The interquartile range is 7 – 3 = 4.

2.5 3 3 4.5 5 5 6 8 14

lower quartile median upper quartile

Find Outliers

Step 2 Multiply the interquartile range by 1.5.

1.5 ● 4 = 6

Step 3 Subtract 6 from the lower quartile and add 6 to the upper quartile.

3 – 6 = –3 7 + 6 = 13

Answer: The only outlier is 14 because it is greater than 13.

A. A

B. B

C. C

D. D

A. 49 is the only outlier.

B. 49 and 15 are outliers.

C. 15 is the only outlier.

D. There are no outliers.

Find any outliers in the data set.

Use Measures of Variation

SOCCER The table shows the number of tickets sold to soccer games at a local stadium. Use the measures of variation to describe the data.

Find the measures of variation.

The range is 301 – 98 = 203.

Use Measures of Variation

The interquartile range is 274 – 184 or 90.

Answer: The spread of the data is 203 tickets. The median number of tickets is 241. The least fourth of the ticket sales is 184 tickets or less. The greatest fourth of ticket sales is 274 or more. The number of tickets sold for half of the games was between 184 and 274.

A. A

B. B

C. C

D. D

A. The spread of the data was 1.05 hours.

B. The median number of hours was 0.59 hour.

C. The greatest fourth of time was 0.66 hour or more.

D. The number of hours exercised for half of the time was between 0.5 hour and 0.66 hour.

On the chart below, Mark kept track of the number of hours he exercised. Which statement is not true?

Measures of Variation

A. LAND USE The urban land in certain Western and Eastern states is listed below as the percent of each state’s total land, rounded to the nearest percent. Compare the western states’ range with the eastern states’ range.

2|0 = 2%

Western States4 3 2 2 2 2 1

5 4

Eastern States

6 6 7 80 3 4 57

0012

2|7 = 27%

Measures of Variation

Answer: The range for the western states is 4%. The range for the eastern states is 21%. The percents of urban land use in the East vary more.

Measures of Variation

B. LAND USE The urban land in certain Western and Eastern states is listed below as the percent of each state’s total land, rounded to the nearest percent. Does the data for either region contain an outlier?

2|0 = 2%

Western States4 3 2 2 2 2 1

5 4

Eastern States

6 6 7 80 3 4 57

0012

2|7 = 27%

Measures of Variation

Answer: There are no outliers for the western states. Since 27 is greater than 26.5, 27 is an outlier for the eastern states.

Western States Eastern StatesLower Quartile: 2 6.5Upper Quartile: 4 14.5Interquartile Range: 4 – 2 = 2 14.5 – 6.5 = 8Multiply by 1.5: 2 ● 1.5 = 3 8 ● 1.5 = 12Determine Outliers: 2 – 3 = –1 x 6.5 – 12 = –5.5

x 4 + 3 = 7 x 14.5 + 12 = 26.5

Measures of Variation

C. LAND USE The urban land in certain Western and Eastern states is listed below as the percent of each state’s total land, rounded to the nearest percent. How does the outlier affect the measures of central tendency for the Eastern States?

2|0 = 2%

Western States4 3 2 2 2 2 1

5 4

Eastern States

6 6 7 80 3 4 57

0012

2|7 = 27%

Measures of Variation

Calculate the mean, median, and mode without the outlier, 27, in the data for the eastern states.

without the outlier with the outlier

median: 9 median: 10

mode: 6 mode: 6

Answer: The mean and median are higher with the outlier. The mode does not change.

A. A

B. B

C. C

D. D

A. teenagers: 21 hr; twenties: 28 hrThe hours of the twenties group vary more.

B. teenagers: 15 hr; twenties: 16 hrThe hours of the twenties group vary only slightly more.

C. teenagers: 22.5 hr; twenties: 24 hrThe hours of the twenties group vary only slightly more.

D. teenagers: 5 hr; twenties: 12 hrThe hours of the twenties group vary more.

A. EXERCISE The hours per week spent exercising for teenagers and people in their twenties are listed in the stem-and-leaf plot. Compare the range for each set of data.

Teens5 4 2 0

7 31

Twenties0 4 6 7 90 2 2 50 3 4 5 8

012

3|1 = 13 hr 1|5 = 15 hr

A. A

B. B

C. C

D. D

A. yes; teens

B. yes; twenties

C. yes; both groups contain an outlier.

D. No; neither group contains an outlier.

B. EXERCISE The hours per week spent exercising for teenagers and people in their twenties are listed in the stem-and-leaf plot. Does the data for either group contain an outlier?

Teens5 4 2 0

7 31

Twenties0 4 6 7 90 2 2 50 3 4 5 8

012

3|1 = 13 hr 1|5 = 15 hr