Question

A student got marks in $5$ subjects in a monthly test is $2,3,4,5,6$ in these obtained marks $4$ is the
A) Mean and median
B) Median but no mean
C) Mean but no median
D) Mode

Answer 1

Hint: For the given problem, we need to find the mean and median to check the correct option. The data is already arranged in ascending order. We must use the mathematical formula of mean and median to find them.

Formula used: Mean is the average value of the given dataset. It is obtained by adding all the observations and dividing them with the total number of observations.
\[{\text{Mean = }}\dfrac{{{\text{Total of all items}}}}{{{\text{Number of items}}}}\]
Median is obtained by arranging the data in ascending order.
Here, the number of observations is \[n = 5\].
Thus, the median will be ${\left( {\dfrac{{n + 1}}{2}} \right)^{th}}$ observation.

Complete step-by-step solution:
Here, we need to compute the mean for the given data. The dataset is $2,3,4,5,6.$\[{\text{Mean = }}\dfrac{{{\text{Total of all items}}}}{{{\text{Number of items}}}}\]
So, Mean $\dfrac{{2 + 3 + 4 + 5 + 6}}{5} = 4$
Thus, \[{\text{4}}\] is the mean of this data set
The student has got \[{\text{4}}\] as an average. Now, we need to calculate the median that is the middlemost value of the dataset.
We need to arrange the data in an ascending order.
So we can write it as, $2,3,4,5,6.$
It is already in ascending order.
So, median $ = {\left( {\dfrac{{n + 1}}{2}} \right)^{th}}$ observation
Here \[n = 5\],
\[ \Rightarrow {\left( {\dfrac{{5 + 1}}{2}} \right)^{th}}\] Observation
On adding the numerator term and we get,
\[ \Rightarrow {3^{rd}}\]Observation
Thus, the value of the given data i.e. \[{\text{4}}\]
Hence the mean and median are equal to \[{\text{4}}\]

Hence the correct option is A.

Note: We need to calculate both mean and median to check whether they are equal to not. Mean and median are important measures of central tendency along with mode. These measures help to analyse the spread and central clustering of the data set. Mean is very easy to calculate and it is affected by the extreme values in the given dataset. It is not the case for median and mode. They both are not affected by extreme values.