A population consists of all the weights of all defensive tackles on Sociable University's football team. They are: Johnson, 204 pounds; Patrick, 215 pounds; Junior, 207 pounds; Kendron, 212 pounds; Nicko, 214 pounds; and Cochran, 208 pounds. What is the population standard deviation (in pounds)?
A) About 4
B) About 16
C) About 100
D) About 40
E) Zero

Question

Quizplus · Accepted Answer

The population standard deviation is calculated by taking the square root of the variance. The variance is the average of the squared differences from the Mean. Here, the mean weight = (204 + 215 + 207 + 212 + 214 + 208) / 6 = 1260 / 6 = 210. The squared differences from the mean are: (204-210)^2, (215-210)^2, (207-210)^2, (212-210)^2, (214-210)^2, (208-210)^2, which are 36, 25, 9, 4, 16, and 4 respectively. The average of these squared differences (variance) = (36+25+9+4+16+4) / 6 = 94 / 6 ≈ 15.67. The square root of 15.67 (standard deviation) is about 4.

A Population Consists of All the Weights of All Defensive