Question

Which of the following, in case of a discrete data is not equal to the median?
A. $50^{th}$ percentile
B. ${5^{th}}$ decile
C. ${2^{nd}}$ quartile
D. lower quartile

Answer 1

Hint: Find the meaning of each given option and equate it with the median to get the required answer.

Complete step by step solution:
Let’s find out the meaning of each given option.
Option A: $50^{th}$ percentile
$50^{th}$ percentile is the second or median quartile of an arranged data set. It splits the data set in half. Hence, it is called the median of a data set.

Option B: ${5^{th}}$ decile
If an ordered data set is divided into $10$ parts, then cut points are called the decile.
${5^{th}}$ decile divides the arranged data set in half. Hence, it is called the median of the data set.

Option C: ${2^{nd}}$ quartile
The ${2^{nd}}$ quartile splits the arranged data set in half. $50\% $ of the data lies below this point. So, it is called the median of the data set.

Option D: lower quartile
The lower quartile is the middle number between the lower half of the arranged data set. It is the median of the lower half of the data set.
Therefore, the lower quartile is not equal to the median.

Option ‘D’ is correct

Note: The median is the middle value of the data when the data is arranged in an ascending or descending order.