Finding Standard Deviation from a Frequency Distribution. In Exercises 37-40, refer to the frequency distribution in the given exercise and compute the standard deviation by using the formula below, where x represents the class midpoint, f represents the class frequency, and n represents the total number of sample values. Also, compare the computed standard deviations to these standard deviations obtained by using Formula 3-4 with the original list of data values: (Exercise 37) 18.5 minutes; (Exercise 38) 36.7 minutes; (Exercise 39) 6.9 years;

(Exercise 40) 20.4 seconds.

Standard deviation for frequency distribution

s=

n= (f. x2)] - [E(f •x)12

n(n - 1)

Age of president at First Inauguration (years)

40-44

45-49

50-54

55-59

60-64

65-69

70-74

Frequency

2

7

10

10

6

3

1