JEE Mains · Maths · STD 11 - 13. statistics
If the mean and variance of the following data: \(6,10,7,13, a, 12, b, 12\) are 9 and \(\frac{37}{4}\) respectively, then \((a-b)^{2}\) is equal to:
- A \(12\)
- B \(24\)
- C \(16\)
- D \(32\)
Answer & Solution
Correct Answer
(C) \(16\)
Step-by-step Solution
Detailed explanation
\(\text { Mean }=\frac{6+10+7+13+a+12+b+12}{8}=9\) \(60+a+b=72\) \(a+b=12\) \(\text { veriance }=\frac{\sum x_{i}^{2}}{n}-\left(\frac{\sum x_{i}}{n}\right)=\frac{37}{4}\) \(\sum x_{i}^{2}=6^{2}+10^{2}+7^{2}+13^{2}+a^{2}+b^{2}+12^{2}+12^{2}\) \(=a^{2}+b^{2}+642\)…
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