If a dataset has a single outlier, which of these measures of spread will be affected if the outlier changes?

(a) Range
(b) Variance
(c) Interquartile Range
(d) Standard Deviation

1 Answer
Geoff K.
Oct 20, 2017

The Interquartile Range (IQR).

Explanation:

All the other measures of spread depend on the value of the outlier:

Range = (largest value) #-# (smallest value)
Variance = #(sum(x_i-barx)^2)/(n-1)#
Standard deviation = #sqrt("Variance")#

The IQR does not. It only depends on where the middle 50% of data points lie. If the outlier shifts slightly, all other measures of spread will change, but the IQR does not change.

Related questions
Impact of this question
318 views around the world
You can reuse this answer
Creative Commons License