Determine the standard deviation of the following sample of survey data: 3, 1, 5, 4, 5
A) 2.80
B) 2.24
C) 1.50
D) 1.67

Question

Quizplus · Accepted Answer

To find the standard deviation of a sample, first calculate the mean (average) of the data. The mean is (3+1+5+4+5)/5 = 3.6. Next, find the squared differences from the mean: (3-3.6)², (1-3.6)², (5-3.6)², (4-3.6)², (5-3.6)². These are 0.36, 6.76, 1.96, 0.16, and 1.96 respectively. The sum of these squared differences is 11.2. Divide this sum by the number of data points minus one (n-1 = 4) to get the variance: 11.2/4 = 2.8. The standard deviation is the square root of the variance: √2.8 ≈ 1.67.

Determine the Standard Deviation of the Following Sample of Survey