1. If for some x E R, the frequency distribution of the marks obtained by 20 students in a test is :

Question:

If for some $\mathrm{x} \in \mathrm{R}$, the frequency distribution of the marks obtained by 20 students in a test is :

then the mean of the marks is :

  1. 2.8

  2. 3.2 

  3. 3.0 

  4. 2.5 


Correct Option: 1

Solution:

$\sum \mathrm{f}_{\mathrm{i}}=20=2 \mathrm{x}^{2}+2 \mathrm{x}-4$

$\Rightarrow \mathrm{x}^{2}+2 \mathrm{x}-24=0$

$\mathrm{x}=3,-4$ (rejected)

$\overline{\mathrm{x}}=\frac{\sum \mathrm{x}_{\mathrm{i}} f_{\mathrm{i}}}{\sum f_{\mathrm{i}}}=2.8$

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