Question

The sum of the mean and median of $4,6,3,1,5$is?
$\left( A \right)0.6$
$(B)7.8$
$\left( C \right)8.0$
$\left( D \right)8.5$

Answer 1

Hint: This is simple mean and median problem by using simple formulas,
$ \Rightarrow $Mean:$\dfrac{{sd}}{N}$_ _ _ _ _ _ _ _ _ _ _ _$\left( 1 \right)$
$ \Rightarrow $Median:$\dfrac{{\left( {N + 1} \right)}}{{2th\_term\_of\_the\_series}}$_ _ _ _ _ _ _ _ _ _ _ $\left( 2 \right)$

Complete step-by-step answer:
Mean refers to the average amount in a given group of data. In this measure of central tendency, all the data are added up and then divided by the number of figures in the data in order to ascertain the mean.
So, the formula of mean is,
$ \Rightarrow $Mean:$\dfrac{{sd}}{N}$
$ \Rightarrow $Mean$ = \left( {\dfrac{{4 + 6 + 3 + 1 + 5}}{5}} \right)$
$ \Rightarrow $Mean$ = 3.8$
Median is the middle most value of a series. So when the series has an odd number of elements then the median can be calculated easily but when the series has an even number of elements then the series has two middle values, so the median is calculated by taking out the average of both the values.
So, the formula is,
$ \Rightarrow $Median:$\dfrac{{\left( {N + 1} \right)}}{{2th\_term\_of\_the\_series}}$
The given series is first arranged into ascending:$1,3,4,5,6$
$ \Rightarrow $Median$ = \dfrac{{\left( {5 + 1} \right)}}{{2th\_term}}$
$ \Rightarrow $Median$ = \dfrac{6}{{2th\_term}}$
$ \Rightarrow $Median$ = 3rd\_term$
$ \Rightarrow $Median$ = 4.$
So,
The sum of mean and median is,
$
   \Rightarrow 3.8 + 4 \\
   \Rightarrow 7.8 \;
 $
So, the correct answer is “Option B”.

Note: $ \Rightarrow $While calculating median, the series is first arranged into either ascending or descending order.
$ \Rightarrow $The mean is the average of a data set. The median is the middle of the set of numbers.
$ \Rightarrow $ The mean is located between the extreme values.
$ \Rightarrow $The sum of the deviations is zero.
$ \Rightarrow $When the mean is calculated, a value of zero, if present, must be taken into account.