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Frequency Distributions

If for some x...

Question

If for some $x \in R$ , the frequrency distribution of the marks obtained by $20$ students in a 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 :

2.5

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3.2

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3.0

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2.8

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Solution

The correct option is D $2.8$
Total number of students $= 20$
$\Rightarrow (x + 1)^{2} + 2 x - 5 + x^{2} - 3 x + x = 20 \Rightarrow x^{2} + x - 12 = 0 \Rightarrow (x - 3) (x + 4) = 0 \Rightarrow x = 3$
$∴$ Mean of the marks $= \frac{2 (3 + 1)^{2} + 3 (6 - 5) + 5 (9 - 9) + 21}{20} = 2.8$

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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

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

x \in R

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

\begin{matrix} x & 4 & 6 & 8 & 10 & 12 f & 7 & 3 & 5 & 9 & 5 \end{matrix}

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

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