Question

In a box-and-whisker plot, the interquartile range is a measure of the spread of the middle half of the data. Find the interquartile range for the data set: 10, 3, 7, 6, 9, 12, 13

Answer 1

In statistics, it is imperative to arrange your data entries from least to greatest. That would be the first step of our solution

3  6  7  9  10  12  13

Interquartile range is the difference of the last quartile to the first quartile. Divide your entire data set into four parts. Each division is called a quartile. Its numerical value is the average of its numbers. However, since our data set contains 7 numbers, which is odd, we write the median (middle value) twice. The quartiles are:

3  6 |  7  9 | 9  10 |  12  13

Q₁= (3+6)/2 = 4.5
Q₂ = (7+9)/2 = 8
Q₃ = (9+10)/2 = 9.5
Q₄ = (12+13)/2 = 12.5

The interquatile range is Q₄ - Q₁ = 12.5 - 4.5 = 8