JEE Main 2022 · 25 Jun · Shift 2 · Mathematics Q25

MathematicsInteger+4 / -1Question 25 of 90

If the mean deviation about the mean of the numbers 1, 2, 3, …, $n$ , where $n$ is odd, is $\dfrac{5(n+1)}n$ , then $n$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 21

Mean deviation. For $n=2k+1$ , mean $k+1$ , and $\sum|x_i-\bar x|=2(1+\dots+k)=k(k+1)$ , so MD $=\dfrac{k(k+1)}n$ .

Equation. $k(k+1)=5(n+1)=10(k+1)$ , so $k=10$ , $n=21$ .

Answer: 21

JEE Main 2022 · 25 Jun · Shift 2, Mathematics question 25