JEE Mains · Maths · STD 11 - 13. statistics
If the mean and variance of six observations \(7,10,11,15, a, b\) are \(10\) and \(\frac{20}{3}\), respectively, then the value of \(|a-b|\) is equal to:
- A \(7\)
- B \(11\)
- C \(9\)
- D \(1\)
Answer & Solution
Correct Answer
(D) \(1\)
Step-by-step Solution
Detailed explanation
\(10=\frac{7+10+11+15+a+b}{6}\) \(\Rightarrow a+b=17\) \(\frac{20}{3}=\frac{7^{2}+10^{2}+11^{2}+15^{2}+a^{2}+b^{2}}{6}-10^{2}\) \(a^{2}+b^{2}=145\) Solve \((i)\) and \((ii)\) \(\mathrm{a}=9, \mathrm{~b}=8\) or \(\mathrm{a}=8, \mathrm{~b}=9\) \(|a-b|=1\)
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