The mean and 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 nine among the ten numbers is 599,what is the tenth number?
Answers
Given :- The mean and 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 nine among the ten numbers is 599, what is the tenth number ?
Solution :-
Let us assume that, the 10th number is x .
we know that,
- standard deviation = √[{(sum of square of all numbers)/N} - (mean)²]
- N = Number of terms.
Given that,
→ standard deviation = 2 .
→ Mean = 8 .
→ N = 10 .
→ sum of square of 9 numbers = 599.
→ 10th number = x .
So,
→ sum of square of all 10 numbers = sum of square of 9 numbers + (10th number)² = (599 + x²)
Putting all values now , we get :-
→ 2 = √[{(599 + x²)/10} - (8)²]
Squaring both sides , we get,
→ 4 = {(599 + x²)/10} - (8)²
→ 4 = {(599 + x²)/10} - 64
→ 4 + 64 = (599 + x²)/10
→ 68 * 10 = 599 + x²
→ x² = 680 - 599
→ x² = 81
Square root both sides we get,
→ x = 9 (Ans.)
Hence, the tenth number is 9.
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