Range, IQR, Mean Absolute Deviation

The range is the difference between the highest and lowest values in a data set.

Range = 87 - 53 = 34.

The median is the middle value when the data is arranged in ascending order.

Arrange the data: 32, 47, 49, 53, 54, 66, 67, 71, 72. Median = 54.

Quartiles divide the data into four equal parts. The first quartile (Q1) is the median of the first half, and the third quartile (Q3) is the median of the second half.

IQR = Q3 - Q1.

Q1 = 48, Q3 = 69, IQR = 69 - 48 = 21.

MAD is the average of the absolute differences between each data point and the mean of the data set.

Mean = 8, Absolute differences = [2, 1, 5, 0, 2]. MAD = (2+1+5+0+2)/5 = 2.

Q1 is the median of the lower half of the data set.