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

Answer: A

Sorted original: 3, 5, 6, 8, 9, 10, 13, 14. Adding 15 gives 3, 5, 6, 8, 9, 10, 13, 14, 15.

- Lower quartile (Q1) = median of 3,5,6,8 = (5+6)/2 = 5.5 (unchanged).
- Median changes from (8+9)/2 = 8.5 to 9.
- Upper quartile changes from median of 9,10,13,14 = 11.5 to median of 10,13,14,15 = 13.5.
- Range changes from 14−3 = 11 to 15−3 = 12.

So the lower quartile is not affected.