Question

In the data set below, what is the lower quartile?
$1,2,4,2,5,6,7$
a) $1$
b) $2$
c) $4$
d) $5$

Answer 1

Hint: The lower quartile is the median of the lower half of the median value.
The median of the observation is found by first arranging the given number in ascending order and the average of the middle two numbers if the total number of observations is even. If the total number of observations are odd then the middle number will be the median.

Complete step by step answer:
Given,
 The data set given is $1,2,4,2,5,6,7$ .
We need to arrange this in ascending order $1,2,2,4,5,6,7$
The median is the average of the middle two numbers if the total number of observations is even. If the total number of observations are odd then the middle number will be the median.
Since the total number of data sets is $7$ which is odd, the median is the middle number.
The median is $4$ .
The lower quartile of the median is the lower part of the data set’s median.
The lower part of the data set is $1,2,2$ .
The number of lower parts of the data set is $3$ , which is odd.
Therefore, the middle part is the median,
So the median is $2$ .
The lower quartile is $2$ .

So, the correct answer is “Option b”.

Note:
The median should be calculated correctly. The data set should be arranged in ascending order. Check whether it is lower or higher quartile. The median can also be found by eliminating both last and final values simultaneously. While finding the median always remember to find the number of observations in a given data set.