If the mode for the following frequency distribution is $22$ and $10 > y > x$ , then $y =$

Class
interval 0-10 10-20 20-30 30-40 40-50 Total

Frequency 5 8 10 x y 30

2

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5

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3

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4

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Solution

The correct option is C $5$
Clearly $20 - 30$ is the modal class such that
$f = 10, f_{1} = 8, f_{2} = x$ and $h = 10$
$∴$ Mode $= l + \frac{f - f_{1}}{2 f - f_{1} - f_{2}} \times h$
$∴ 22 = 20 + \frac{10 - 8}{20 - 8 - x} \times 10 \Rightarrow 2 = \frac{20}{12 - x} \Rightarrow x = 2$
It is given that
$5 + 8 + 10 + x + y = 30 \Rightarrow x + y = 7$
Hence, $x = 2$ and $y = 5$

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Similar questions

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33 \frac{1}{3}

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If the median of the distribution is given below is 28.5, find the values of x and y.

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0 − 10	5
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Total	60

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Frequency	$5$	$x$	$6$	$y$	$6$	$5$	$40$

Question 2
If the median of the distribution given below is 28.5, find the values of x and y.

$\begin{matrix} C l a s s i n t e r v a l & F r e q u e n c y 0 - 10 & 5 10 - 20 & x 20 - 30 & 20 30 - 40 & 15 40 - 50 & y 50 - 60 & 5 T o t a l & 60 \end{matrix}$

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Class interval	0-10	10-20	20-30	30-40	40-50	Total
Frequency	5	8	10	x	y	30

If the mode for the following frequency distribution is 22 and 10>y>x, then y= Class interval 0-10 10-20 20-30 30-40 40-50 Total Frequency 5 8 10 x y 30

The correct option is C 5Clearly 20−30 is the modal class such that f=10, f1=8, f2=x and h=10∴ Mode =l+f−f12f−f1−f2×h∴22=20+10−820−8−x×10⇒2=2012−x⇒x=2It is given that5+8+10+x+y=30⇒x+y=7Hence, x=2 and y=5

If the mode for the following frequency distribution is $22$ and $10 > y > x$ , then $y =$

Class
interval 0-10 10-20 20-30 30-40 40-50 Total

Frequency 5 8 10 x y 30