Q75 / 150 · MHT CET 2021 (23 Sep Shift 2) · Mathematics

Given that total of 16 values is 528 and sum of the squares of deviation from 33 is 9158 . The variance is

  • A
    562.73
  • B
    570.375
  • C
    574.375
  • Correct answer
    D
    572.375

Solution

We have $\mathrm{n}=16, \Sigma \mathrm{x}_{\mathrm{i}}=528$, and $\frac{528}{16}=33$ $\Rightarrow \overline{\mathrm{x}}=33$ and $\Sigma\left(\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right)^2=9158$ Variance $=\frac{1}{\mathrm{n}} \Sigma\left(\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right)^2=\frac{9158}{16}=527.375$

Hence, the correct answer is option: 'D'.

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