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# The Mean of 100 Observations is 50 and Their Standard Deviation is 5. the Sum of All Squares of All the Observations Is(A) 50,000 (B) 250,000 (C) 252500 (D) 255000 - Mathematics

MCQ

The mean of 100 observations is 50 and their standard deviation is 5. The sum of all squares of all the observations is

#### Options

•  50,000

•  250,000

• 252500

• 255000

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#### Solution

Let $\bar{ x}$ and $\sigma$  be the mean and standard deviation of 100 observations, respectively.

$\therefore x = 50, \sigma = 5$  and n = 100
Mean,$\bar{ x}$ = 50

$\Rightarrow \frac{\sum_{} x_i}{100} = 50$

$\Rightarrow \sum_{} x_i = 5000 . . . . . \left( 1 \right)$

Now,
Standard deviation,

$\sigma = 5$

$\Rightarrow \sqrt{\frac{\sum_{} x_i^2}{100} - \left( \frac{\sum_{} x_i}{100} \right)^2} = 5$

$\Rightarrow \frac{\sum_{} x_i^2}{100} - \left( \frac{5000}{100} \right)^2 = 25 \left[ \text{ From } \left( 1 \right) \right]$

$\Rightarrow \frac{\sum_{} x_i^2}{100} = 25 + 2500 = 2525$

$\Rightarrow \sum_{} x_i^2 = 252500$

Thus, the sum of all squares of all the observations is 252500.

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 32 Statistics
Q 20 | Page 51
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