JEE MAIN - Mathematics (2019 - 10th April Morning Slot - No. 13)
If for some x $$ \in $$ R, the frequency distribution of the marks obtained by 20 students in a test is :
then the mean of the marks is
| Marks | 2 | 3 | 5 | 7 |
|---|---|---|---|---|
| Frequency | (x + 1)2 | 2x - 5 | x2 - 3x | x |
then the mean of the marks is
3.0
2.8
2.5
3.2
Explanation
Number of students
$$ \Rightarrow {\left( {x + 1} \right)^2} + (2x - 5) + \left( {{x^2} - 3x} \right) + x = 20$$
$$ \Rightarrow 2{x^2} + 2x - 4 = 20$$
$$ \Rightarrow {x^2} + x - 12 = 0$$
$$ \Rightarrow (x + 4)(x - 3) = 0$$
$$x = 3$$
Average marks = $${{32 + 3 + 21} \over {20}} = {{56} \over {20}} = 2.8$$
$$ \Rightarrow {\left( {x + 1} \right)^2} + (2x - 5) + \left( {{x^2} - 3x} \right) + x = 20$$
$$ \Rightarrow 2{x^2} + 2x - 4 = 20$$
$$ \Rightarrow {x^2} + x - 12 = 0$$
$$ \Rightarrow (x + 4)(x - 3) = 0$$
$$x = 3$$
| Marks | 2 | 3 | 5 | 7 |
|---|---|---|---|---|
| No. of students | 16 | 1 | 0 | 3 |
Average marks = $${{32 + 3 + 21} \over {20}} = {{56} \over {20}} = 2.8$$
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