Find the interquartile range of the
set of data: 29.7, 36.2, 29.1, 11.7, 45.3, 19.6, 42.8, 57.9, 51.9, 42.9, 51.2, 5.4,
29.2, 15.4, and 11.6.
The first thing that we should do
is put these numbers in ascending order, smallest to largest. Our smallest number is 5.4, then
11.6, then 11.7. Next is 15.4, then 19.6, then
29.1. Next is 29.2, now 29.7, 36.2, 42.8,
42.9, 45.3, 51.2, 51.9, and lastly 57.9.
So now we need to find the median,
the middle number. There are 15 total numbers. So what is the middle of 15? That would be eight. There are seven numbers on each
side of that number. So that eighth number would be in
the middle. So 29.7 is our median.
Now our next step is to find the
middle of this lower half and the middle of the upper half. Out of seven numbers, the fourth
one would be the middle because there would be three numbers on each side, so
15.4. And then on the upper half, it
would be 45.3.
So we are finding the interquartile
range. Now let’s think about this:
quartile, four. Here’s one quarter of our numbers,
another quarter or quartile, a third, and a fourth. So the interquartile range is the
range between the interquartiles. So we need to take 45.3 and
subtract 15.4, resulting in an interquartile range of 29.9.