Q 83. - The Practice of Statistics for AP

Question

Incomes of college grads According to the Census Bureau, the mean and median $2008$ income of people at least $25$ years old who had a bachelor’s degree but no higher degree were $\backslash (48,097$ and $\backslash )60,954$ Which of these numbers is the mean and which is the median? Explain your reasoning. 

Step-by-Step Solution

Answer

The mean is 

$\begin{array}{rcl}\overline{x}& =& \$60954\\ Median& =& \$48097\end{array}$

Step 1: Given Information

The median is $ 60,954 while the mean is $48,097.

Step 2: Concept

The total of all observations divided by the number of observations is the observation mean. The median of a distribution organised in ascending order is the midway.

Step 3: Calculation

The majority of those with a bachelor's degree (but no higher) will earn the same amount, while some will earn significantly more.

As a result, the salary distribution will be right-skewed.

We know that the mean is bigger than the median in a right-skewed distribution because the mean is influenced by extremely high incomes while the median is not: 

$\overline{x}= \$60, 954$

MEDIAN$=\$48, 097$

Therefore, mean is $\$60, 954$and median is $\$48, 097$