Chapter 3.3, Problem 38BSC

Finding Standard Deviation from a Frequency Distribution. In Exercises 37-40, find the standard deviation of sample data summarized in a frequency distribution table 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) 11.1 years; (Exercise 38) 9.0 years; (Exercise 39) 13.4; (Exercise 40) 9.7 years.

$s=\sqrt{\frac{n[{\displaystyle \sum (f\cdot x^2)]-[{\displaystyle \sum (f\cdot x}){]}^2}}{n(n-1)}}$Standard deviation for frequency distribution

38.

Age of Best Actor When Oscar Was Won		Frequency
20-29		1
30-39		26
40-49		35
50-59		13
60-69		6
70-79		1