Question

Find the mean, variance, and standard deviation for the following data set. Round to the nearest tenth. 55, 87, 62, 85, 93, 75

Answer 1

Mean: (55 + 87 + 62 + 85 + 93 + 75) / 6 = 77.8

Variance:
1. Find the squared differences from the mean:
(55-77.8)^2 = 551.24
(87-77.8)^2 = 87.04
(62-77.8)^2 = 247.04
(85-77.8)^2 = 52.84
(93-77.8)^2 = 235.24
(75-77.8)^2 = 7.84

2. Find the sum of the squared differences:
551.24 + 87.04 + 247.04 + 52.84 + 235.24 + 7.84 = 1181.24

3. Find the variance:
1181.24 / 6 = 196.9

Standard Deviation:
Square root of the variance = sqrt(196.9) = 14.0

Therefore, the mean is 77.8, the variance is 196.9, and the standard deviation is 14.0.