Which one of the values below represents a lower quartile for the data set 23, 24, 21, and 20?
22, 22.5, 20.5, 23.5, None of these

Solution:

Given: Data set is 23, 24, 21, and 20

The lower quartile, or first quartile, is denoted as Q1 and is the middle number that falls between the smallest value of the dataset and the median,

In other words it is the lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order.

Let us arrange the given data set in increasing order as 20, 21, 23, 24

Median of the given set is the midpoint of 21 and 23 as the number of data is even.

M = (21 + 23)/2 = 44/2 = 22

The median of the left side values of M is Q1.

Q1 = (20+21)/2 = 41/2

=20.5

Hence, the lower quartile of a given data set is 20.5

Which one of the values below represents a lower quartile for the data set 23, 24, 21, and 20?

Summary:

Number 20.5 represents a lower quartile for the data set 23, 24, 21, and 20.