Hoaglin, Mosteller, and Tukey (1983) presented data on blood levels of beta-endorphin as a function of stress. They took beta-endorphin levels for 19 patients 12 hours before surgery and again 10 minutes before surgery. The data are presented below. Does there appear to be a difference in the mean level of beta endorphins present? Participant 12 hours before 10 minutes before 1 10 6.5 2 6.5 14.0 3 8.0 13.5 4 12 18 5 5.0 14.5 6 11.5 9.0 7 5.0 18.0 8 3.5 42.0 9 7.5 7.5 10 5.8 6.0 11 4.7 25.0 12 8.0 12.0 13 7.0 52.0 14 17.0 20.0 15 8.8 16.0 16 17.0 15.0 17 15.0 11.5 18 4.4 2.5 19 2.0 2.0

Hoaglin, Mosteller, and Tukey (1983) presented data on blood levels of beta-endorphin as a function of stress. They took beta-endorphin levels for 19 patients 12 hours before surgery and again 10 minutes before surgery. The data are presented below. Does there appear to be a difference in the mean level of beta endorphins present? Participant 12 hours before 10 minutes before 1 10 6.5 2 6.5 14.0 3 8.0 13.5 4 12 18 5 5.0 14.5 6 11.5 9.0 7 5.0 18.0 8 3.5 42.0 9 7.5 7.5 10 5.8 6.0 11 4.7 25.0 12 8.0 12.0 13 7.0 52.0 14 17.0 20.0 15 8.8 16.0 16 17.0 15.0 17 15.0 11.5 18 4.4 2.5 19 2.0 2.0

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Description: Hoaglin, Mosteller, and Tukey (1983) presented data on blood levels of beta-endorphin as a function of stress. They took beta-endorphin levels for 19 patients 12 hours before surgery and again 10 minutes before surgery. The data are presented below.

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Hoaglin, Mosteller, and Tukey (1983) presented data on blood levels of beta-endorphin as a function of stress. They took beta-endorphin levels for 19 patients 12 hours before surgery and again 10 minutes before surgery. The data are presented below. Does there appear to be a difference in the mean level of beta endorphins present?

Participant 12 hours before 10 minutes before

1 10 6.5

2 6.5 14.0

3 8.0 13.5

4 12 18

5 5.0 14.5

6 11.5 9.0

7 5.0 18.0

8 3.5 42.0

9 7.5 7.5

10 5.8 6.0

11 4.7 25.0

12 8.0 12.0

13 7.0 52.0

14 17.0 20.0

15 8.8 16.0

16 17.0 15.0

17 15.0 11.5

18 4.4 2.5

19 2.0 2.0

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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