EXAMPLE 11 Finding Quartiles

The city mileages of the 12 gasoline-powered midsized cars, after sorting, are

We have indicated with brackets a split of the data into a lower half and an upper half. The first quartile is the median of the six observations in the lower half, so . Similarly, the third quartile is the median of the upper half: .

For an example with an odd number of observations, try the city mileages of all 13 midsized cars in Table 5.7 (page 196). Below are the mileages in increasing order, with the median in the center, which will be excluded to form two equal-sized groups:

We find the quartiles by finding the median of each half of the dataset: and .

Some software packages or calculators may use a slightly different procedure to find the quartiles, so their results may be a bit different from our work here. Don’t worry about this. The differences will be too small to be important.