Question

If each number in a given data is reduced by 15%, then the median will be

• A. Increased by 15%
• B. 15 times
• C. Reduced by 15%
• D. Remain same

Answer 1

The correct option is C Reduced by 15%

Given that each number in the given data is reduced by 15%.
Let n be the number of observations and x be the median.
If n is odd, then x is $(\frac{n+1}{2}{)}^{th}$ term of the observations, which is reduced by 15%.
Thus, x is reduced by 15%.
If n is even, then
x = $\frac{(\frac{n}{2}{)}^{th}\text{term}+(\frac{n}{2}+1{)}^{th}\text{term}}{2}$
Let x′ be the new median.
$\therefore x^{\prime }=\frac{85\text{\% of}(\frac{n}{2}{)}^{th}\text{term}+(85\text{\% of}\frac{n}{2}+1{)}^{th}\text{term}}{2}$
$=85\text{\%}\left[\frac{(\frac{n}{2}{)}^{th}\text{term}+(\frac{n}{2}+1{)}^{th}\text{term}}{2}\right]$
$\Rightarrow x\text{'}=85\text{\%}ofx$
Therefore, the new median will be reduced by 15%.
Hence, the correct answer is option (c).