Multiple choice

Mean of $5$ observation is $7$. If four of these observation are $6,7,8,10$ and one is missing then the variance of of all the five observations is :

  1. $4$
  2. $6$
  3. $8$
  4. $2$
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A Correct answer
Explanation

Mean = 7, sum = 35. 6+7+8+10+x = 35 => 31+x = 35 => x = 4. Observations: 4, 6, 7, 8, 10. Mean = 7. Variance = [(4-7)^2 + (6-7)^2 + (7-7)^2 + (8-7)^2 + (10-7)^2] / 5 = [9 + 1 + 0 + 1 + 9] / 5 = 20 / 5 = 4.

AI explanation

The sum of the five observations is 5 multiplied by 7, which equals 35. Let the missing observation be m, so 6 + 7 + 8 + 10 + m = 35, giving m = 4. The mean is 7, so the squared deviations are (6-7)^2 = 1, (7-7)^2 = 0, (8-7)^2 = 1, (10-7)^2 = 9 and (4-7)^2 = 9. The variance is the sum of these squared deviations divided by 5, which is 20 divided by 5, equaling 4.

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