If for some x \[ \in \] R, the frequency distribution of the marks obtained by 20 students in a test is :
Marks
2
3
5
7
Frequency
(x + 1)2
2x - 5
x2 - 3x
x
then the mean of the marks is
Solutions · 1
Official solution
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
Marks
2
3
5
7
No. of students
16
1
0
3
Average marks = \[{{32 + 3 + 21} \over {20}} = {{56} \over {20}} = 2.8\]