KCET · Maths · Statistics
The mean and standard deviation of \(100\) items are \(50\) and \(4\), respectively then the sum of all squares of the items is
- A \(250000\)
- B \(251600\)
- C \(256100\)
- D \(265100\)
Answer & Solution
Correct Answer
(B) \(251600\)
Step-by-step Solution
Detailed explanation
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: \(251600\)
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