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  • The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased from 8 to 12 . If the new mean of the marks is

The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased from 8 to 12 . If the new mean of the marks is 10.2, then their new variance is equal to :

Option: 1

3.96


Option: 2

4.08


Option: 3

4.04


Option: 4

3.92


Answers (1)

best_answer

Let Number of observations is =\underline{\mathrm{n}}

\begin{aligned} & \frac{\sum x_{i}}{n}=10 \quad \frac{\sum x_{i}-8+12}{n}=10.2 \\ & \sum \mathrm{x}_{\mathrm{i}}=10 \mathrm{n} \\ & 10 \mathrm{n}=(10.2) \mathrm{n}-4 \\ & \Rightarrow(.2) \mathrm{n}=4 \quad \Rightarrow \quad \mathrm{n}=20 \end{aligned}

Given \frac{\sum \mathrm{x}_{\mathrm{i}}^{2}}{20}-(10)^{2}=4 \quad \Rightarrow \sum \mathrm{x}_{\mathrm{i}}^{2}=2080

After Change
                    \sum \mathrm{x}_{\mathrm{i}}^{2} =2080-8^{2}+(12)^{2}
                                  =2160

\text{New vanance} =\frac{\sum \mathrm{x}_{\mathrm{i}}^{2}}{20}-(\overline{\mathrm{x}})^{2}
                             =\frac{2160}{20}-(10.2)^{2}
                            =108-(10.2)^{2}
                            =3.96

 

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