The standard deviation of the set 21, 23, 24, 25, 27 is approximately 2.000 g/mile and the variance is approximately 4.002 g^2/mile^2.
Calculate the mean: (21 + 23 + 24 + 25 + 27) / 5 = 24
Calculate the squared deviations from the mean for each data point:
(21 - 24)^2 = 9
(23 - 24)^2 = 1
(24 - 24)^2 = 0
(25 - 24)^2 = 1
(27 - 24)^2 = 9
Calculate the variance:
Sum the squared deviations: 9 + 1 + 0 + 1 + 9 = 20
Divide the sum by the number of data points (n-1): 20 / (5-1) = 4.002 g^2/mile^2
Calculate the standard deviation:
Take the square root of the variance: √4.002 ≈ 2.000 g/milemilemilemile