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  4. The mean marks obtained by 300 students in Mathematics are 45. The mean of top 100 Students was 70 and the mean of last 100 was known to be 20. The mean of remaining 100 students is

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Q. The mean marks obtained by $300$ students in Mathematics are $45.$ The mean of top $100$ Students was $70$ and the mean of last $100$ was known to be $20.$ The mean of remaining $100$ students is

NTA AbhyasNTA Abhyas 2022

Solution:

$45=\frac{70 \times 100 + \bar{x}_{2} \times 100 + 100 \times 20}{300}$
$\Rightarrow 135=90+\bar{x}_{2}\Rightarrow \bar{x}_{2}=45$