Q75 / 160 · TS EAMCET 2019 (03 May Shift 1) · Mathematics

In a data with 15 number of observations $x_1$, $x_2, x_3, \ldots, x_{15}, \sum_{i=1}^{15} x_i^2=3600$ and $\sum_{i=1}^{15} x_i=175$. If the value of one observation 20 was found wrong and was replaced by its correct value 40 , then the corrected variance of that data is

  • Correct answer
    A
    151
  • B
    149
  • C
    145
  • D
    144

Solution

Given, $$ \sum_{i=1}^{15} x_i^2=3600, \sum_{i=1}^{15} x_i=175 $$ When 20 is replace by 40 , then $$ \begin{gathered} \sum_{i=1}^{15} x_i=175-20+40=195 \\ \sum_{i=1}^{15} x_i^2=3600-(20)^2+(40)^2=4800 \\ \therefore \text { Corrected variance }=\frac{\sum x_i^2}{n}-\left(\frac{\sum x_i}{n}\right)^2 \\ =\frac{4800}{15}-\left(\frac{195}{15}\right)^2=320-169=151 \end{gathered} $$

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

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