Question

The mode and median of the following data $21,23,25,23,21,24,22,20,23$ respectively, are
A) $23,23$
B) $21,23$
C) $25,21$
D) $23,21$

Answer 1

At first, we will arrange the data into ascending and descending order. Then by the definition of median and mode we can find the value of the median and mode. The most frequent number occurring in the data set is known as the mode. To find the value of median we will apply the formula according to the number of terms.

Complete step-by-step solution:
The given data are: $21,23,25,23,21,24,22,20,23$
We have to find the mode and median.
We know that the most frequent number occurring in the data set is known as the mode.
Let us arrange the data in ascending order: $20,21,21,22,23,23,23,24,25$.
Here, $23$ occurs thrice.
So, the mode of the given data is $23$.
Here, the total number of terms is $9$.
We know that, if number of values or observations in the given data is odd, then the median is given by ${\left( {\dfrac{{n + 1}}{2}} \right)^{th}}$ observation.
Since, the number of terms is odd, the median is $= {\left( {\dfrac{{9 + 1}}{2}} \right)^{th}}$ term $= {5^{th}}$ term $= 23$
So, the mode and median of the given data is $23,23$.

Hence, the correct option is A.

Note: Generally median represents the mid value of the given set of data when arranged in a particular order.
Given that the data collection is arranged in ascending or descending order, the following method is applied
If number of values or observations in the given data is odd, then the median is given by ${\left( {\dfrac{{n + 1}}{2}} \right)^{th}}$ observation.
If in the given data set, the number of values or observations is even then the median is given by the average of ${\left( {\dfrac{n}{2}} \right)^{th}}$ and ${\left( {\dfrac{n}{2} + 1} \right)^{th}}$ observation.
The most frequent number occurring in the data set is known as the mode.