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AP EAMCET · Maths · Statistics

The mean deviation from the mean of the series \((a),(a+d),(a+2 d), \ldots \ldots \ldots . .,(a+2 n d)\) is

  1. A \(\frac{n(n-1) d}{2 n+1}\)
  2. B \(\frac{n(n+1) d}{2 n+1}\)
  3. C \((n(n+1) d)\)
  4. D \(\frac{n(n+1) d}{2 n}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{n(n+1) d}{2 n+1}\)

Step-by-step Solution

Detailed explanation

The mean of given series \(a, a+d, a+2 d, \ldots \ldots, a+2 n d\) is \(\frac{\frac{2 n+1}{2}[2 a+(2 n) d]}{2 n+1}=(a+n d)=m\) (let) So, the mean deviation \(=\frac{1}{2 n+1} \sum_{i=1}^{2 n+1}\left|x_i-m\right|\)…