Question

What is the sample standard deviation for the data set: 3, 5, 7, 5, 6, 9, 11, 8, 12
O 2.96
O 7.3
07
O 2.79

Answer 1

To calculate the sample standard deviation for the data set, we first need to find the mean (average) of the data set.

Mean = (3 + 5 + 7 + 5 + 6 + 9 + 11 + 8 + 12) / 9 = 66 / 9 = 7.33

Next, we calculate the differences between each data point and the mean, square those differences, sum them, divide by n-1, and then take the square root.

(3 - 7.33)^2 = 18.2089
(5 - 7.33)^2 = 5.4156
(7 - 7.33)^2 = 0.1089
(5 - 7.33)^2 = 5.4156
(6 - 7.33)^2 = 1.7689
(9 - 7.33)^2 = 2.7889
(11 - 7.33)^2 = 13.4644
(8 - 7.33)^2 = 0.4489
(12 - 7.33)^2 = 21.4889

Sum of squared differences = 69.3599

Sample variance = 69.3599 / 8 = 8.6699

Sample standard deviation = √8.6699 = 2.9470

Therefore, the sample standard deviation for the data set is approximately 2.95. So, the closest option listed is 2.96.