For $100$ observations following table was prepared
Class $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$
$f_{i}$ $8$ $30$ $b$ $c$ $d$
If median of the distribution is $23$ , then the value of $b$ will be?

30

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20

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40

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Can't be predicted

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Solution

The correct option is D $40$
Class $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$
$f_{i}$ 8 30 b c d
$c f$ 8 38 38+b 38+b+c 38+b+c+d
Number of observations $= 50$
Median $= 23$
Therefore median class is $20 - 30$
Median $= l + ⎛ ⎜ ⎜ ⎝ \frac{\frac{n}{2} - c f}{f} ⎞ ⎟ ⎟ ⎠ h$
$l$ is the lower limit of median class
$c f$ is the cumulative frequency of class preceding the median class
$f$ is frequency of median class
$h$ is class size
Therefore, $23 = 20 + ⎛ ⎜ ⎜ ⎜ ⎝ \frac{\frac{100}{2} - 38}{b} ⎞ ⎟ ⎟ ⎟ ⎠ 10$
$\Rightarrow 3 b = (50 - 38) 10 \Rightarrow 3 b = 120 \Rightarrow b = 40$
So, option C is correct.

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Marks	0−10	10−20	20−30	30−40	40−50
Number of Students	8	30	40	12	10

Marks	0−10	10−20	20−30	30−40	40−50
No. of Students	8	?	40	?	10

f_{1}

f_{2}

N = 100

32

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$T o t a l$
Frequency	$10$	$f_{1}$	$25$	$30$	$f_{2}$	$10$	$100$

Find the missing frequency in the following distribution if $N = 100$ and median is $32$

Marks	0-10	10-20	20-30	30-40	40-50	50-60	Total
No. of students	10	?	25	30	?	10	100

Marks obtained	0−10	10−20	20−30	30−40	40−50	50−60	Total
No. of Students	10	?	25	30	?	10	100

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