Question

Despite tuition skyrocketing, a college education is still valuable. Recent calculations by the Federal Reserve Bank in San Francisco demonstrate a college degree is worth $830,000 in lifetime earnings compared to the average high school education. Assume graduates in 2019 earn $40,632, $35,554, $42,192, $33,432, $69,479 and $43,589. What is the standard deviation for this sample?

Answer 1

Answer:

s = $13,014.22

Explanation:

Sample values: $40,632, $35,554, $42,192, $33,432, $69,479 and $43,589

Sample size = 6

The standard deviation of a sample (s) is given by:

$s=\sqrt{\frac{\sum(x_i-X)^2}{n-1}}$

Where X is the sample mean, n is the sample size, and xi is each value in the sample.

The sample mean is given by:

$X=\frac{\ 40,632 +\ 35,554+\ 42,192 +\ 33,432 +\ 69,479 +\ 43,589}{6} \\X=\ 44,146.33$

The standard deviation is:

$s=\sqrt{\frac{\sum(x_i-\ 44,146.33)^2}{6-1}}\\s=\ 13,014.22$