Compute the Standard Deviation of a Variable from Raw Data
-3, 3, 14, 11, 11, 20, 14, 10, 14
A) 5.4
B) 5.1
C) 29.6
D) 26.3

Question

Quizplus · Accepted Answer

The standard deviation is calculated by first finding the mean (average) of the data, then calculating the squared difference from the mean for each data point, summing those squared differences, dividing by the number of data points to find the variance, and finally taking the square root of the variance. For the given data set: Mean = (3 + 3 + 14 + 11 + 11 + 20 + 14 + 10 + 14) / 9 = 100 / 9 ≈ 11.11. Squared differences from the mean are calculated for each data point, summed, divided by the number of data points (n-1 for sample standard deviation, n for population), and the square root of that result gives the standard deviation. Following these steps for the given data set results in a standard deviation of approximately 5.4, making choice A correct.