JEE Mains · Maths · STD 11 - 13. statistics
If the mean and variance of five observations are \(\frac{24}{5}\) and \(\frac{194}{25}\) respectively and the mean of first four observations is \(\frac{7}{2}\), then the variance of the first four observations in equal to
- A \(\frac{4}{5}\)
- B \(\frac{77}{12}\)
- C \(\frac{5}{4}\)
- D \(\frac{105}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{5}{4}\)
Step-by-step Solution
Detailed explanation
\(\bar{X}=\frac{24}{5} ; \sigma^2=\frac{194}{25}\) Let first four observation be \(\mathrm{x}_1, \mathrm{x}_2, \mathrm{x}_3, \mathrm{x}_4\) Here, \(\frac{x_1+x_2+x_3+x_4+x_5}{5}=\frac{24}{5}\). Also, \(\frac{\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3+\mathrm{x}_4}{4}=\frac{7}{2}\)…
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