12.3 Hank Aaron. Here are Aaron’s home run counts for his 23 years in baseball:
| 13 | 27 | 26 | 44 | 30 | 39 | 40 | 34 | 45 | 44 | 24 | 32 |
| 44 | 39 | 29 | 44 | 38 | 47 | 34 | 40 | 20 | 12 | 10 |
Find the mean and standard deviation of the number of home runs Aaron hit in each season of his career. How do the mean and median compare?
12.3 To find the mean,
To find the standard deviation, use a table layout:
| Observation | Squared distance from mean |
|---|---|
| 13 | (13 − 32.83)2 = (−19.83)2 |
| = 393.2289 | |
| 27 | (27 − 32.83)2 = (−5.83)2 |
| = 33.9889 | |
| ⋮ | |
| 10 | (10 − 32.83)2 = (−22.83)2 |
| = 521.2089 | |
| sum = 2751.3200 |
The variance is the sum divided by n − 1, which is 23 − 1, or 22.
630
The standard deviation is the square root of the variance.
The mean (32.83) is less than the median of 34. This is consistent with the fact that the distribution of Aaron’s home runs is slightly left-skewed.