Q 84. - The Practice of Statistics for AP

Question

House prices: The mean and median selling prices of existing single-family homes sold in November $2009$ were $\backslash (216,400$ and $\backslash )172,600$. Which of these numbers is the mean and which is the median? Explain how you know.

Step-by-Step Solution

Answer

 $$\begin{gathered} Mean=\$216,400 \\ Median: \$172600 \end{gathered}$$

Step 1: Given Information

The mean and median selling prices of existing single-family homes sold in November$2009$ were $\$216,400$ and $\$172,600$

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

Existing single-family homes sold for $\$216,400$ and $\$172,600$, respectively.

The majority of residences will sell for around the same amount, while others will sell for significantly more.

As a result, the selling price 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:

 $$\begin{gathered} \overline{x} = \$216, 400 \\ MEDIAN =\$172, 600 \end{gathered}$$