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JEE Main 202225 JuneEvening Shift
Exam
JEE Main
Year
2022
Date
25 June
Shift
Evening Shift
Subject
Mathematics
Chapter
Statistics

JEE Main 2022 · 25 June · Evening Shift · Mathematics · Statistics

If the mean deviation about the mean of the numbers 1, 2, 3, , n ,...

If the mean deviation about the mean of the numbers 1,2,3,……,n1, 2, 3, \ldots \ldots , n, where nn is odd, is 5(n+1)n\dfrac{5\left(n + 1\right)}{n}, then nn is equal to ______.

Correct answer

0

Step-by-step solution

We know that mean deviation about the mean of odd natural number is given by M.D\text{M.D}\left(x\right) = \dfrac{1}{n}[n2−14]\left[\dfrac{{n}^{2} - 1}{4}\right]

So, now 1n[n2−14]=5(n+1)n\dfrac{1}{n}\left[\dfrac{{n}^{2} - 1}{4}\right] = \dfrac{5\left(n + 1\right)}{n} (given)

⇒n−1=20⇒n=21⇒ n - 1 = 20 ⇒ n = 21

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