6.7Use Measures of Central Tendency Example 1 Compare measures of central tendency Temperature The daily February temperatures (in degrees Fahrenheit)

6.7 Use Measures of Central Tendency

Example 1 Compare measures of central tendencyCompare measures of central tendency

Temperature The daily February temperatures (in degrees Fahrenheit) for 10 days are listed for a certain city. Find the mean, median, and mode(s) of the data.

Solution20, 21, 22, 24, 25, 26, 27, 29, 37, 37

37372927262524222120 x

10

26810

_____ 26.8


Example 1 Compare measures of central tendencyCompare measures of central tendency

Temperature The daily February temperatures (in degrees Fahrenheit) for 10 days are listed for a certain city. Find the mean, median, and mode(s) of the data.

Solution20, 21, 22, 24, 25, 26, 27, 29, 37, 37

The median is the mean of the two middle values, ______.25.5

The mode is ______.37

The ______ and ________ best represent the data.mean median

6.7 Use Measures of Central TendencyCheckpoint. Complete the following exercises. Checkpoint. Complete the following exercises. 1. Find (a) the mean, (b) the median,

and (c) the mode(s) of the data set. 67, 70, 73, 73, 78, 80

807873737067 a

x

6 6

441 5.73

37 b

37 c


Example 2 Compare measures of dispersionCompare measures of dispersionRunning The top 4 finishing times (in seconds) for two different teams in the 50 meter dash are given. Compare the spread of the data for the two sets using (a) the range and (b) the mean absolute deviation.

Solution

Team A: 5.8, 6.0, 6.2, 6.4 Team B: 5.7, 5.9, 6.5, 6.7

a. Team A: ____ _____ = _____ 6.4 5.8 0.6Team B: ____ _____ = _____ 6.7 5.7 1

The range for Team ___ is greater than the range for Team ___, so the data for Team ___ cover a wider interval than the data for Team ___.

BA B

A



Solution

Team A: 5.8, 6.0, 6.2, 6.4 Team B: 5.7, 5.9, 6.5, 6.7

b. The mean for Team A is ____, so the mean absolute deviation is:6.1

4

1.64.61.62.61.60.61.68.5 .____ 0.2

The mean for Team B is ____, so the mean absolute deviation is:6.2

4

2.67.62.65.62.69.52.67.5 .____ 0.4



Solution

Team A: 5.8, 6.0, 6.2, 6.4 Team B: 5.7, 5.9, 6.5, 6.7

The mean absolute deviation of Team ___ is greater, so the average variation from the mean is greater for the data for Team ___ than for the data for Team ___.

B

B A

6.7 Use Measures of Central TendencyCheckpoint. Complete the following exercises. Checkpoint. Complete the following exercises. 2. In Example 2, suppose the slowest time

for Team B was 6.6 seconds. Recalculate the range and mean absolute deviation.Team B: 5.7, 5.9, 6.5, 6.6

Range: 7.56.6 = 0.9

Mean absolute deviation: mean is 6.175

4

175.66.6175.65.6175.69.5175.67.5

0.3754

425.0325.0275.0475.0

4

5.1


Pg. 385, 6.7 #1-19

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6.7Use Measures of Central Tendency Example 1 Compare measures of central tendency Temperature The daily February temperatures (in degrees Fahrenheit)