Question

The length of ribbons found at a seamstress are listed.

2, 10, 10, 12, 12, 20

What is the appropriate measure of variability for the data shown, and what is its value?

The mean is the best measure of variability and equals 11.
The median is the best measure of variability and equals 11.5.
The range is the best measure of variability and equals 18.
The IQR is the best measure of variability and equals 2.

Answer 1

Therefore, the appropriate measure of variability for this data set is the IQR, and its value is 2.

Explanation:

The range is the simplest measure of variability and is the difference between the largest and smallest values. In this case, the largest value is 20 and the smallest value is 2, so the range is:

Range = 20 - 2 = 18

However, since there are some extreme values (2 and 20), it may be better to use a measure of variability that is less affected by outliers. The interquartile range (IQR) is a good measure of variability that is less affected by extreme values.

To find the IQR, we need to find the median of the data set. The median is the middle value when the data is arranged in order. In this case, the data set has an even number of values, so the median is the average of the two middle values:

Median = (10 + 12) / 2 = 11

Next, we need to find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half of the data set, and Q3 is the median of the upper half of the data set. In this case, the lower half of the data set is {2, 10, 10} and the upper half of the data set is {12, 12, 20}.

Q1 = Median of lower half = 10

Q3 = Median of upper half = 12

So, the IQR is:

IQR = Q3 - Q1 = 12 - 10 = 2

Therefore, the appropriate measure of variability for this data set is the IQR, and its value is 2.