Question

Does it appear to you that the only time an outlier might change the median is if the sample is small?

Why or why not?

Give an example of where an outlier may well change the median, and please use something different than the real estate market. In fact, see if you can come up with something in the manufacturing area.

Answer 1

(a)

The only time an outlier might change the median is if the sample is small.

REASON: The median represents a point value above and below which 50 % of the values fall. The median is positional in rank order and so it is only influenced by a value only if the sample is small.

(b)

EXAMPLE OF OUTLIER CHANGING MEDIAN IN MANUFACTRING AREA:

Diameters (in mm) of 5 "O" rings used in a manufacturing industry: 3.5, 5.2, 4.5, 5.7, 3.1

To find the median:
Arranging numbers in ascending order:

3.1,3.5,4.5,5.2,5.7

Median = (n+1)/2 = (5+1)/2=3rd value. = 4.5

So,

Median = 4.5

Adding an outlier, we get the new set as:

3.1, 3.5, 4.5, 5.2, 5.7, 10

New median = (n+1)/2 = (6+1)/2 = average of 3rd & 4th value = (4.5 + 5.2)/2 =4.85

We note that the median has gone up from 4.5 to 4.85 because of outlier = 10, since it is small sample.