EXAMPLE 20 Mean Family Size
The first two rows in Table 8.8 give a probability distribution for U.S. family size, . (Although there are some families that have more than eight members, the likelihood is so small that we ignored this possibility in the discrete probability model.) The third row shows Step 3 in the procedure for calculating the mean—it contains the products of family size and corresponding probability.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
|---|---|---|---|---|---|---|---|---|
| 0.15 | 0.23 | 0.19 | 0.23 | 0.12 | 0.05 | 0.02 | 0.01 | |
| 0.15 | 0.46 | 0.57 | 0.92 | 0.6 | 0.3 | 0.14 | 0.08 |
To calculate the mean, simply sum the entries in the third row:
In Chapter 5 (page 197), we discussed the sample mean , the average of observations that we actually have in hand. Take, for example, the data below on family size from a random sample of 30 families in the United States.
In this case, the sample mean is computed by summing the data values and dividing by 30: .