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Frequency Distributions

If for some ...

Question

If for some $x \in R$ , the frequency distribution of the marks by $20$ students in test is:
Marks 2 3 5 7
Frequency $(x + 1)^{2}$ $(2 x - 5)$ $x^{2} - 3 x$ $x$
then the mean of the marks is:

2.8

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3.2

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3.0

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2.5

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Solution

The correct option is A $2.8$
$\sum f_{i} = 20 = 2 x^{2} + 2 x - 4$
$\Rightarrow x^{2} + 2 x - 24 = 0$
$x = 3, - 4$ (rejected)
$¯ x = \frac{\sum x_{i} f_{i}}{\sum f_{i}} = 2.8$

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Similar questions

x \in R

20

Marks	$2$	$3$	$5$	$7$
Frequency	$(x + 1)^{2}$	$2 x - 5$	$x^{2} - 3 x$	$x$

x \in R

20

Marks	$2$	$3$	$5$	$7$
Frequency	$(x + 1)^{2}$	$2 x - 5$	$x^{2} - 3 x$	$x$

28

40

Marks	0-10	10-20	20-30	30-40
Number of students	6	$x$	$y$	6

20

x

y

60

\begin{matrix} Marks & Frequency 0 & x - 2 1 & x 2 & x^{2} 3 & (x + 1)^{2} 4 & 2 x 5 & x + 1 \end{matrix}

x

Marks (x):	5	10	15	20	25	30	35	40	45	50
No. of students (f):	15	50	80	76	72	45	39	9	8	6

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