1. Measures of Center and Variation

2. Sample mean
Example: The birth weights in pounds: 9.2, 6.4, 10.5, 8.1, 7.8.
The mean is ( ) / 5 = 8.4
Figure 2.9 (p. 42) Dot diagram and the sample mean for the birth-weight data.

3. Sample median
Example(cont.): The birth weights in pounds: 9.2, 6.4, 10.5, 8.1, 7.8.
The median is 8.1 .
Note: The median is not affected by a few very small or very large observations, whereas the presence of such extremes can have a considerable effect on the mean.

4. The sample 100 p-th percentile is a value such that after the data are ordered from smallest to largest, at least 100p % of the observations are at or below this value and at least 100(1-p) % are at or above this value.

5. An example of percentiles
To determine the first quartile
take p=.25
38 * .25 = 9.5
round 9.5 up to 10
10th ordered observation is 4.4
so the first quartile is Q1 = 4.4

6. Figure 2.10 (p. 49) Dot diagrams with similar center values but different amounts of variation.

7. Box on Page 50 Sample variance of n observations

8. Table 2.10 (p. 50) Calculation of Variance

9. Box on Page 51 Sample Standard Deviation
To obtain a measure of variability in the same unit as the data, take the positive square root of the variance:
Box on Page 51 Sample Standard Deviation

10. Other measures of variation
Example of phone calls (table 8): Sample range = 53.3 – 1.6 = 51.7
Note: sample range is very sensitive to the existence of a very large or very small observation in the data set.
Example of phone calls: Sample interquartile range = 17.5 – 4.4 = 13.1

11. Boxplots
The center half of the data, from the first to the third quartile, is represented by a rectangle (box) with the median indicated by a bar.
A line extends from Q3 to the maximum value and another from Q1 to the minimum.
Figure (p. 55) Boxplot of the length of phone call data in Table 8