The median of the following data is 525. Find the missing frequency, if it is given that there are 100 observations in the data:
Class interval Frequency Class interval Frequency
$0 - 100$ 2 $500 - 600$ 20
$100 - 200$ 5 $600 - 700$ $f_{2}$
$200 - 300$ $f_{1}$ $700 - 800$ 9
$300 - 400$ 12 $800 - 900$ 7
$400 - 500$ 17 $900 - 1000$ 4

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Solution

Class interval Frequency Cumulative frequency

0 – 100 2 2

100 – 200 5 7

200 – 300 f₁ 7 + f₁

300 – 400 12 19 + f₁

400 – 500 17 36 + f₁(F)

500 – 600 20 (f) 56 + f₁

600 – 700 f₂ 56 + f₁ + f₂

700 – 800 9 65 + f₁ + f₂

800 – 900 7 72 + f₁ + f₂

900 – 1000 4 76 + f₁ + f₂

$N$ = $100$

Given

Median = $525$

Then, median class = $500 - 600$

$L$ = $500$ , $f$ = $20$ , $F$ = 36 + f_{1 ,} $h$ = $600 - 500$ = $100$
$Median space equals space L plus fraction numerator begin display style N over 2 end style minus F over denominator f end fraction cross times h 525 space equals space 500 plus fraction numerator 50 minus left parenthesis 36 plus f subscript 1 right parenthesis over denominator 20 end fraction cross times 100 525 space equals space 500 space plus fraction numerator 50 minus 36 minus f subscript 1 over denominator 20 end fraction cross times 100 25 space equals space left parenthesis 14 space â�� space f subscript 1 right parenthesis space cross times space 5$
$5$ = 14 – f₁
f₁= 14 – 5 = 9

Given

Sum of frequencies = $100$

2 + 5 + f₁ + 12 + 17 + 20 + f₂ + 9 + 7 + 4 = $100$

2 + 5 + 9 + 12 + 17 + 20 + f₂ + 9 + 7 + 4 = $100$

$85$ + f₂= $100$

f₂ = 100 – 85 = 15

f₁= 9 and f₂= 15

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Similar questions

Q. The median of the following data in

525

. Find the missing frequency, if it is given that there are

100

observations in the data:

Class interval	Frequency	Class interval	Frequency
0-100	$2$	500-600	$20$
100-200	$5$	600-700	$f_{2}$
200-300	$f_{1}$	700-800	$9$
300-400	$12$	800-900	$7$
400-500	$17$	900-1000	$4$

Q. The median of the following data is 525. Find the missing frequency, if it is given that there are 100 observation in the data:

Class interval	Frequency	Class interval	Frequency
0−100 100−200 200−300 300−400 400−500	2 5 f₁ 12 17	500−600 600−700 700−800 800−900 900−1000	20 f₂ 9 7 4

Q. The median of the following data is

525

. Find the values of

x

and

y

, if the total frequency is

100

Class interval	Frequency
$0 - 100$	$2$
$100 - 200$	$5$
$200 - 300$	$x$
$300 - 400$	$12$
$400 - 500$	$17$
$500 - 600$	$20$
$600 - 700$	$y$
$700 - 800$	$9$
$800 - 900$	$7$
$900 - 1000$	$4$

Q. Find the mean of the following data .

Class Interval	Frequency
$0 - 100$	$2$
$100 - 200$	$5$
$200 - 300$	$4$
$300 - 400$	$12$
$400 - 500$	$17$
$500 - 600$	$20$
$600 - 700$	$20$
$700 - 800$	$9$
$800 - 900$	$7$
$900 - 1000$	$4$

The median of the following data is 525. Find the values of x and y, if the total frequency is 100.

$\begin{matrix} C l a s s I n t e r v a l & F r e q u e n c y 0 - 100 & 2 100 - 200 & 5 200 - 300 & x 300 - 400 & 12 400 - 500 & 17 500 - 600 & 20 600 - 700 & y 700 - 800 & 9 800 - 900 & 7 900 - 1000 & 4 \end{matrix}$ [4 MARKS]

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Class interval	Frequency	Cumulative frequency
0 – 100	2	2
100 – 200	5	7
200 – 300	f₁	7 + f₁
300 – 400	12	19 + f₁
400 – 500	17	36 + f₁(F)
500 – 600	20 (f)	56 + f₁
600 – 700	f₂	56 + f₁ + f₂
700 – 800	9	65 + f₁ + f₂
800 – 900	7	72 + f₁ + f₂
900 – 1000	4	76 + f₁ + f₂
	$N$ = $100$