Question

Despite tuition skyrocketing, a college education is still valuable. Recent calculation by the federal reserve bank in San Francisco demonstrate a college degree is worth $800,000 in lifetime earnings compared to the average high school education. Assume graduates in 2017 earn $40,632,$35,554,$42,192,$33,432,$69,479, and $43,598. What is the variance for this sample? ( Round your intermediate calculations and final answer to the nearest whole number.)​

Answer 1

Answer:

The variance is: $169,367,949

Step-by-step explanation:

Given

Tuition: $40,632, $35,554, $42,192, $33,432, $69,479, and $43,598

Required

Determine the variance

First, calculate the mean

$\bar x = \frac{\sum x}{n}$

Where

$n =6$

$\bar x = \frac{40,632+35,554+42,192+33,432+69,479+43,598}{6}$

$\bar x = \frac{264,887}{6}$

$\bar x = 44147.8333333$

$\bar x = 44148$ --- approximated

The sample variance (s^2) is calculated using:

$s^2 = \frac{\sum(x - \bar x)^2}{n-1}$

This gives:

$s^2 = \frac{(40,632-44148)^2+(35,554-44148)^2+(42,192-44148)^2+(33,432-44148)^2+(69,479-44148)^2+(43,598-44148)^2}{6-1}$

$s^2 = \frac{846839745}{5}$

$s^2 = 169367949$

The variance is: $169,367,949