The mean and the standard deviation of a data which is comprised of a set of…
2026
The mean and the standard deviation of a data which is comprised of a set of ten positive numbers are 8 and 2 respectively. If the sum of squares of 9 among the 10 members is 599,what is the 10th number.
- A.
10
- B.
9
- C.
5
- D.
8
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Correct answer: B
Let the 10th number be x.
For the population standard deviation, variance satisfies:
σ² = (sum of squares of all terms)/N − μ²
Given μ = 8, σ = 2 and N = 10, so
4 = (Σxi²)/10 − 64 ⇒ (Σxi²)/10 = 68 ⇒ Σxi² = 680.
The sum of squares of nine numbers is 599, so x² = 680 − 599 = 81.
All numbers are positive, hence x = 9.