A sample of 12 students was asked how many hours they had studied the week before their final exam.

Question

Their responses were as follows:

18 40 14 23 14 15 18 14 19 13 16 12

A) Discuss the effect on the mean of removing the outlier from the given

data.

Answer 1

An outlier causes the mean to be skewed excessively.

It makes the students look like they studied more than they really did. With an outlier, the median is a better measure of the average than the mean.

An outlier can be removed if it appears unreliable or impossible or unlikely, to get a better more reliable statistic.

A student may be pretending to study 40 hours when they really didn't.

If they claimed they studied 100 hours in a week, that would be so suspect, you'd want to remove it from the data.

Answer 2

Hi Sarah!

Let's discuss what outliers do in general. For your reference, this is the definition of an outlier in Wolfram alpha: "an outlier is a point which falls more than 1.5 times the interquartile range above the third quartile or below the first quartile."

What does this mean? An outlier will either shift the mean up or down - depending on whether it is 1.5*the interquartile range above the third quartile (shift up), or 1.5 times the interquartile range below the first quartile (shift down). So for this problem, determine your quartiles to find the outlier, and determine if it shifts the mean up or down. Removing the outlier will give you the opposite shift.

(Note - I don't know what course you are taking; outliers can also be defined using standard deviation).