Medians and IQRs. For each part, compare distributions (1)

Problem 1.46

Medians and IQRs. For each part, compare distributions (1) and (2) based on their medians and IQRs. You do not need to calculate these statistics; simply state how the medians and IQRs compare. Make sure to explain your reasoning.

(a) (1) 3, 5, 6, 7, 9 (2) 3, 5, 6, 7, 20

(b) (1) 3, 5, 6, 7, 9 (2) 3, 5, 7, 8, 9

c) (1) 1, 2, 3, 4, 5 (2) 6, 7, 8, 9, 10

(d) (1) 0, 10, 50, 60, 100 (2) 0, 100, 500, 600, 1000

                                                             Step by step solution

Step 1 of 4

(a)

(1) 3, 5, 6, 7, 9

(2) 3, 5, 6, 7, 20

If the data are ordered from smallest to largest, the median is the observation right in the middle. There are 5 data values so the median will be the middle value, ie; 6, for both the data sets.

The first quartile  is the 25th percentile, i.e. 25% of the data, between the first two values. The third quartile,   is the 75th percentile, ie; between the last two values.

The Interquartile range (IQR) is difference between the third quartile and first quartile, ie;

IQR =

Therefore, Medians are equal for (1) & (2), but IQR is higher for distribution (2) because the third quartile of distribution (2) is greater than distribution (1)..