Q128 / 240 · KCET 2026 · Mathematics
The mean and standard deviation of $100$ items are $50$ and $4$, respectively then the sum of all squares of the items is
- A$250000$
- Correct answerB$251600$
- C$256100$
- D$265100$
Solution
Given $n = 100$, $\bar{x} = 50$, and $\sigma = 4$.
The formula for variance is $\sigma^2 = \dfrac{\sum x_i^2}{n} - (\bar{x})^2$.
Substituting the given values:
$4^2 = \dfrac{\sum x_i^2}{100} - (50)^2$
$16 = \dfrac{\sum x_i^2}{100} - 2500$
$\dfrac{\sum x_i^2}{100} = 2516$
$\sum x_i^2 = 251600$
Answer: $251600$
The formula for variance is $\sigma^2 = \dfrac{\sum x_i^2}{n} - (\bar{x})^2$.
Substituting the given values:
$4^2 = \dfrac{\sum x_i^2}{100} - (50)^2$
$16 = \dfrac{\sum x_i^2}{100} - 2500$
$\dfrac{\sum x_i^2}{100} = 2516$
$\sum x_i^2 = 251600$
Answer: $251600$
Hence, the correct answer is option: 'B'.