Question

Which element of variation would not be affected by adding the data value 15 to the data set {3, 5, 6, 8, 9, 10, 13, 14}?
A.
the lower quartile of the data set
B.
the median of the data set
C.
the upper quartile of the data set
D.
the range of the data set

Answer 1

A. The lower quartile.

Original set (n=8): Q1 = 5.5, median = 8.5, Q3 = 11.5, range = 14−3 = 11.
After adding 15 (n=9): Q1 = 5.5 (unchanged), median = 9, Q3 = 13.5, range = 15−3 = 12.
Only the lower quartile stays the same.