Chapter 3.2, Problem 40BSC

Finding Standard Deviation from a Frequency Distribution. In Exercises 37-40, refer to the frequency distribution in the given exercise and find 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) 11.5 years; (Exercise 38) 8.9 years; (Exercise 39) 59.5; (Exercise 40) 65.4.

Standard deviation for frequency distribution

$s=\sqrt{\frac{n\left[\Sigma \left(f\cdot x^2\right)\right]-{\left[\Sigma \left(f\cdot x\right)\right]}^2}{n\left(n-1\right)}}$

40.