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

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.

Is there an error in this question or solution?

APPEARS IN

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