Multiple choice

The sum of deviations of $n$ observations about $25$ is $25$ and the sum of deviations of the same $n$ observations about $35$ is $-25$. The mean of observations is

  1. $25$
  2. $30$
  3. $35$
  4. $40$
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B Correct answer
Explanation

Sum(xi - 25) = 25 => Sum(xi) - 25n = 25. Sum(xi - 35) = -25 => Sum(xi) - 35n = -25. Subtracting equations: 10n = 50 => n = 5. Sum(xi) = 25 + 25(5) = 150. Mean = 150 / 5 = 30.

AI explanation

The sum of deviations of observations about a value equals n times the mean minus n times that value. From the first condition, 25 equals n times the mean minus 25n. From the second condition, -25 equals n times the mean minus 35n. Solving these simultaneous equations gives n equals 5 and the mean equals 30.

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