What percentage of data is above the first quartile? Circle your answer. Is it 25 percent, 37.5 percent, 50 percent, or 75 percent?
There are two possible ways of measuring the spread of a data set. The first is to find the range. To do that, we subtract the smallest value from the largest value. The second is to find the interquartile range. To do that, we subtract the lower quartile from the upper quartile. But what do we mean by the word quartile?
Well, a quartile is one-quarter of the way through the data. This means that the lower quartile or the first quartile is one-quarter of the way through the data, whereas the upper quartile — that’s the third quartile — is three-quarters through the data.
Now, for this question, we’re interested in knowing what proportion of the data set lies above the first quartile. Now, if we recall one-quarter is the same as 25 percent. So the first quartile is 25 percent of the way through the data.
To find the percentage of the data that lies above this quartile then, we’ll subtract 25 percent from 100 percent since 100 percent is all of the data. 100 minus 25 is 75.
And that tells us that 75 percent of the data is above the first quartile.