Question

what is the third quartile of this data set? 14, 18, 20, 21, 25, 32, 38, 42, 48
a. 42
b. 38
c. 40
d. 36

Explanation:

Step1: Arrange data in ascending order

The data is already in ascending order: 14, 18, 20, 21, 25, 32, 38, 42, 48.

Step2: Calculate the position of the third - quartile

The formula to find the position of the third - quartile ($Q_3$) for a data set of size $n$ is $i=\frac{3(n + 1)}{4}$. Here, $n = 9$.
$i=\frac{3\times(9 + 1)}{4}=\frac{3\times10}{4}=7.5$.

Step3: Interpolate to find $Q_3$

Since the position is 7.5, $Q_3$ is the value that is 0.5 between the 7th and 8th ordered data values. The 7th value is 38 and the 8th value is 42.
$Q_3=38+(42 - 38)\times0.5=38 + 2=40$.

Answer:

C. 40