Example 2.15 from Statistics, 2.3 Measures of the Location of the Data

Measures of the Location of the Data: example 2.15

For the following 13 real estate prices, calculate the IQR and determine if any prices are potential outliers. Prices are in dollars.
389,950; 230,500; 158,000; 479,000; 639,000; 114,950; 5,500,000; 387,000; 659,000; 529,000; 575,000; 488,800; 1,095,000

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Order the following data from smallest to largest:
114,950; 158,000; 230,500; 387,000; 389,950; 479,000; 488,800; 529,000; 575,000; 639,000; 659,000; 1,095,000; 5,500,000
M = 488,800
Q₁ = $\frac{230,500 + 387,000}{2}$ = 308,750
Q₃ = $\frac{639,000 + 659,000}{2}$ = 649,000
IQR = 649,000 – 308,750 = 340,250
(1.5)(IQR) = (1.5)(340,250) = 510,375
Q₁ – (1.5)(IQR) = 308,750 – 510,375 = –201,625
Q₃ + (1.5)(IQR) = 649,000 + 510,375 = 1,159,375

No house price is less than –201,625. However, 5,500,000 is more than 1,159,375. Therefore, 5,500,000 is a potential outlier.

How did it go?

Solution

Solution