Question

Housing Prices An Erie, PA, newspaper advertised homes for sale in different areas of the region. In Summit Township, seven homes were advertised at the following listing prices: $199,000, $109,000, $229,000, $169,900, $219,900, $25,500, and $207,000. In the rural area south of Summit, six homes were advertised at the following listing prices: $749,000, $352,400, $314,900, $165,000, $175,000, and $215,000.

• (a) Find the mean and median housing prices for Summit Township.

• (b) Find the mean and median housing prices for the rural area.

• (c) Discuss the differences between the mean and median for each region. Which gives a truer representation of the average housing price for each region?

Answer 1

a)
Summit township
25500
109000
169900
199000
207000
219900
229000
Mean = (25500 + 109000 + 169900 + 199000 + 207000 + 219900 + 229000) / 7
Mean = 165,614.29
Median = 199,000
b)
Rural area
165000
175000
215000
314900
352400
749000
Mean = (165000 + 175000 + 215000 + 314900 + 352400 + 749000) / 6
Mean = 328,550
Median = (215000+314900)/2
Median = 264950
c)
Difference between the mean and median of Summit township= 165614.29-199000
Difference between the mean and median of Summit township = -33385.71
Difference between the mean and median of Summit township = 328550-264950
Difference between the mean and median of Summit township = 63600
As the difference between average and median for Summit township is lower than the rural area Summit township gives truer picture the average housing price.
Formula
Mean = Sum of all values / Number of values
Median = Midpoint of values