Find the interquartile range for the given set of data.

{30, 24, 8, 21, 35, 23, 23, 19, 13, 17}

{30, 24, 8, 21, 35, 23, 23, 19, 13, 17}

The interquartile range (IR) of a given set of data is IR = Q3-Q1.

To simply the comprehension, we can put the data in ascending order:

8, 13, 17, 19, 21, 23, 23, 24, 30, 35

From there, it is easier to find the quartiles of this set.

The first quartile (Q1) is the middle value of the first half of the rank-ordered set of data, while the third quartile (Q3) is the middle value of the second half. So we need to find the middle of the whole set (Q2), also known as the median.

With an odd set of numbers, this median is the middle value:

(n/2) + 1 where x is the number of data. E. g If there are three numbers, the median is the second one of the ascending order of the set.

But in this case, with an even set of numbers, the median is simply between the two middle values : between (n/2) and (n/2) + 1. In this case, between the 5th and 6th numbers.

8, 13, 17, 19, 21 | 23, 23, 24, 30, 35

Since Q2 has no direct value, its indirect value comes from the average of the two numbers around it (only with an even set of numbers).

Now we need to find our values Q1 and Q3. Q1 is the middle value of the first half. In this case : Q1 = 17. Q3 = 24. The interquartile range then is:

IR = Q3-Q1

IR = 24-17

IR = 7