The mean of the series x1, x2...xn is x̅ If xn is replaced by k, then what is the new mean?

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NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. x̅ - xn + k
  2. \(\rm \frac{n\bar x-\bar x+k}{n}\)
  3. \(\rm \frac{\bar x-x_n-k}{n}\)
  4. \(\rm \frac{n\bar x-x_n+k}{n}\)

Answer (Detailed Solution Below)

Option 4 : \(\rm \frac{n\bar x-x_n+k}{n}\)
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Detailed Solution

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Explanation:

Given:

\(\overline x = \frac{x_1+x_2+x_3+......... x_n}{n}\)

⇒ \(x_1+x_2+X_3+......x_n= n\overline x \)

⇒ Mean when xn is replaced by k

⇒ New mean = \(\frac{x_1+x_2+x_3+......... x_{n-1}+k}{n}\)

\(\frac{n\overline x -x_n+k}{n}\)

∴ Option (d) is correct

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