Question

Find the variance and the standard deviation of the following set: 5,6,7,8,9 If necessary, round to the nearest hundredth.

Answer 1

Explanation:

Calculate the mean: (5 + 6 + 7 + 8 + 9) / 5 = 7

Calculate the squared deviations from the mean for each data point:

(5 - 7)^2 = 4

(6 - 7)^2 = 1

(7 - 7)^2 = 0

(8 - 7)^2 = 1

(9 - 7)^2 = 4

Calculate the variance:

Sum the squared deviations: 4 + 1 + 0 + 1 + 4 = 10

Divide the sum by the number of data points (n-1): 10 / (5-1) = 2

Calculate the standard deviation:

Take the square root of the variance: √2 ≈ 1.41



Therefore, the variance of the set is 2.00 and the standard deviation is 1.41, both rounded to the nearest hundredthhundredth