Measures of the Location of the Data: example 2.17

Using the data from the frequency table, we have the following:

1. The 80^th percentile is between the last eight and the first nine in the table (between the 40^th and 41^st values). Therefore, we need to take the mean of the 40^th an 41^st values. The 80^th percentile $=\frac{8+9}{2}=8.5\text{.}$
2. The 90^th percentile will be the 45^th data value (location is 0.90(50) = 45), and the 45^th data value is nine.
3. Q₁ is also the 25^th percentile. The 25^th percentile location calculation: P₂₅ = .25(50) = 12.5 ≈ 13, the 13^th data value. Thus, the 25^th percentile is six.