EXAMPLE 11Calculating the variance and standard deviation of a discrete random variable
The probability distribution for the number of credits is repeated here as Table 5. In Example 7, we calculated the mean number of credits as . Calculate the variance and standard deviation.
12 | 0.1 |
13 | 0.1 |
14 | 0.1 |
15 | 0.5 |
16 | 0.1 |
20 | 0.1 |
Solution
Refer to Table 6. The first two columns correspond to the probability distribution of . The third column represents the calculations needed to find . Summing the values in the rightmost column provides the variance . Taking the square root of the variance gives us the standard deviation credits.
320
credits
12 | 0.1 | |
13 | 0.1 | |
14 | 0.1 | |
15 | 0.5 | |
16 | 0.1 | |
20 | 0.1 | |
NOW YOU CAN DO
Exercises 53a,b–60a,b.