JEE Mains · Maths · STD 11 - 13. statistics
For a statistical data \(\mathrm{x}_1, \mathrm{x}_2, \ldots, \mathrm{x}_{10}\) of 10 values, a student obtained the mean as 5.5 and \(\sum_{i=1}^{10} x_i^2=371\). He later found that he had noted two values in the data incorrectly as 4 and 5 , instead of the correct values 6 and 8 , respectively. The variance of the corrected data is
- A \(9\)
- B \(5\)
- C \(7\)
- D \(4\)
Answer & Solution
Correct Answer
(C) \(7\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Mean } \overline{\mathrm{x}}=5.5 \\ & =\sum_{\mathrm{i}=1}^{10} \mathrm{x}_{\mathrm{i}}=5.5 \times 10=55 \\ & =\sum_{\mathrm{i}=1}^{10} \mathrm{x}_{\mathrm{i}}^2=371 \\ & \left(\sum \mathrm{x}_{\mathrm{i}}\right)_{\text {new }}=55-(4+5)+(6+8)=60 \\ & \\…
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