Using the given box-and-whisker plot, find the interquartile range of the data.
And the data is talking about the number of fish in various ponds. Before we find the interquartile range, let’s look at the main pieces of data in this set.
The minimum is found at this point — so 75. And minimum means that’s the smallest number found in this set. So the smallest number of fish found in these ponds is 75. And the largest number of fish in these various ponds will be 250 because this is the maximum — the largest number in the set. The median is considered the middle number. So 125 will be the middle number in this set.
So if 125 is the middle number, that means the lower half of the data. So 50 percent of the data is between 75 and 125. So half of these ponds have between 75 and 125 fish. So the upper half — so 50 percent of the data — means that the other half of the ponds must have between 125 fish and 250 fish.
And now for these points, the lower quartile and the upper quartile, these are considered in the middle of the halves. So 100 is our lower quartile and 225 is our upper quartile. So if these numbers are in the middle of the halves, then on each side would be 25 percent because we’re splitting the 50 percent in half, which we can see here and here. And this makes sense because 25 plus 25 plus 25 plus 25 is 100, making the full 100 percent of data.
So back to finding the interquartile range, this is taking the upper quartile and subtracting the lower quartile. The upper quartile was 225 and the lower quartile was 100. And 225 minus 100 means that our interquartile range is 125.