Find the standard deviation of the sample data summarized in
Find the standard deviation of the sample data summarized in a frequency distribution table by using the formula below, where equation represents the class midpoint, equation represents the class frequency, and equation represents the total number of sample values. Standard deviation for frequency distribution: equation .
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
Solution
First fill the intervals without gap and then prepare the table as follows:
Variance = 1/n (sum of fx^2) -Mean ^2
Std dev = square root of variance
| Interval | Corrected CI | Mid point | freq | ||
| x | f | fx | fx^2 | ||
| 20-29 | 19.5-29.5 | 24.5 | 1 | 24.5 | 600.25 |
| 34.5 | 26 | 897 | 30946.5 | ||
| 44.5 | 35 | 1557.5 | 69308.75 | ||
| 54.5 | 13 | 708.5 | 38613.25 | ||
| 64.5 | 6 | 387 | 24961.5 | ||
| 74.5 | 1 | 74.5 | 5550.25 | ||
| 82 | 3649 | 169980.5 | |||
| Average | 44.5 | 2072.933 | |||
| Variance | 92.68293 | ||||
| Std dev | 9.627197 |
