6.8Compare Statistics from Samples Example 1 Compare statistics from different samples Production The data set below give the number of computers assembled

6.8 Compare Statistics from Samples

Example 1 Compare statistics from different samplesCompare statistics from different samples

Production The data set below give the number of computers assembled by each employee during one month in the East production division and the West production division. Compare the data using the mean, median, range, and interquartile range.East: 19, 18, 17, 16, 15, 13, 12, 10 West: 21, 20, 19, 18, 17, 16, 14, 9

East West

___8

10 19

x 15 _____

8

9 21

x 16.75




East WestMedian: Median:

____2

15.51516

____2

17.51718




East WestRange: Range:

_________ 919 10 _________ 1221 9




East WestLower Quartile: Lower Quartile:

____2

12.51213

____2

151416




East WestUpper Quartile: Upper Quartile:

____2

17.51718

____2

19.51920




East WestInterquartile Range: Interquartile Range:

_________ 55.17 5.12 _________ 4.55.19 15




The _______ mean is greater than the _______ mean, so the ______ averaged more computers assembled per person.

West’s East’sWest

The East’s _______ is less than the West’s, so their data is less spread out.

range




The West’s ___________________ is _____ than the East’s, so the West’s middle 50% of the data showed _____ variation than the middle 50% of the East’s data.

interquatile range lessless


Example 2 Compare sample and population statisticsCompare sample and population statistics

Production At the end of the month, summary production statistics are calculated for the entire company. The table below shows the summary data for the North and South divisions. Find the averages of the summary statistics from the four samples: the East and West divisions from Example 1, the North division and the South division.

Mean Median Range Interquartile Range

North

South

All

5.17 5.15 7 3

3.13 12 11 6

9.14 13 10 5.5

________

x




North

South

All

5.17 5.15 7 3

3.13 12 11 6

9.14 13 10 5.5

Average Mean:Solution

15 16.75 17.5 13.34

6375.15

________




North

South

All

5.17 5.15 7 3

3.13 12 11 6

9.14 13 10 5.5

Average Median:Solution

15.5 17.5 15.5 124

125.15

________




North

South

All

5.17 5.15 7 3

3.13 12 11 6

9.14 13 10 5.5

Average Range:Solution

9 12 7 114

75.9

________




North

South

All

5.17 5.15 7 3

3.13 12 11 6

9.14 13 10 5.5

Average Interquartile Range:Solution

5 4.5 3 64

625.4




North

South

All

5.17 5.15 7 3

3.13 12 11 6

9.14 13 10 5.5Solution

The average mean and median are _____ than the corresponding population measures. The average range and interquartile range are _____ than the corresponding population measures.

more

less

6.8 Compare Statistics from SamplesCheckpoint. Complete the following exercises. Checkpoint. Complete the following exercises. 1. Compare the data using the mean, median, range,

and interquartile range. Data set 1: 102, 105, 108, 110, 112, 113Data set 2: 100, 103, 105, 106, 109, 113


Data set 1

Data set 2

3.108

650x

6636

x6

106

109

5.105

113range 102

11

113range 100

13

112range int. 105

7

109range int. 103

6

6.8 Compare Statistics from SamplesCheckpoint. Complete the following exercises. Checkpoint. Complete the following exercises. 2. In Example 2, suppose the Northeast division had the

following statistics. How does the inclusion of the Northeast division’s statistics change the averages in Example 2?


Northeast 7.15 18 12 2.7

Averages

25.78x

5

65.15

5.785

7.15

515

2.10

7.255

14.5

The average mean, median, and range are higher than the corresponding population measures. The average interquartile range is lower than the corresponding population measures.


Pg. 391, 6.8 #1-7

Documents

6.8Compare Statistics from Samples Example 1 Compare statistics from different samples Production The data set below give the number of computers assembled