The birthrates in the country for the years 1981-1990 are: (The birthrate is the number of live births/1,000 population.) Compute the mean, variance, and standard deviation of the random variable X.

Question

The birthrates in the country for the years 1981-1990 are:  (The birthrate is the number of live births/1,000 population.) Compute the mean, variance, and standard deviation of the random variable X.

Quizplus · Accepted Answer

To compute the mean, we add up all the birthrates and divide by the total number of years:
(16.7 + 16.5 + 16.7 + 16.3 + 15.8 + 15.5 + 15.2 + 14.7 + 14.4 + 14.0)/10 = 15.64

To compute the variance, we need to find the squared deviations from the mean, sum them up, and divide by the total number of years:
[(16.7-15.64)^2 + (16.5-15.64)^2 + (16.7-15.64)^2 + (16.3-15.64)^2 + (15.8-15.64)^2 + (15.5-15.64)^2 + (15.2-15.64)^2 + (14.7-15.64)^2 + (14.4-15.64)^2 + (14.0-15.64)^2]/10
= 0.52424

To compute the standard deviation, we take the square root of the variance:
sqrt(0.52424) = 0.724

Therefore, the best choice is B, with mean 15.64, variance 0.52424, and standard deviation 0.724.

The Birthrates in the Country for the Years 1981-1990 Are