Question

in the data set below, what is the lower quartile? 1 2 2 4 7 7 8

Explanation:

Step1: Count data points

There are 7 data - points: 1, 2, 2, 4, 7, 7, 8.

Step2: Calculate position of lower quartile

The formula for the position of the lower quartile ($Q_1$) for a data - set with $n$ data points is $L=\frac{n + 1}{4}$. Here, $n = 7$, so $L=\frac{7+1}{4}=2$.

Step3: Find the lower quartile

Since the position $L = 2$ is an integer, the lower quartile is the 2nd value in the ordered data - set. The 2nd value in the ordered data - set 1, 2, 2, 4, 7, 7, 8 is 2.

Answer:

2