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.

Table 6.10: Table 5Probability distribution of the number of credits
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

Table 6.11: Table 6Calculating and
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.