An incomplete distribution is given below:
Variable
Frequency
$10 - 20$
$12$
$20 - 30$
$30$
$30 - 40$
$f_{1}$
$40 - 50$
$65$
$50 - 60$
$f_{2}$
$60 - 70$
$25$
$70 - 80$
$18$
If median value is $46$ and the total number of items is $230$ .
Find the missing frequencies $f_{1}$ and $f_{2}$ .

40 & 46

No worries! We‘ve got your back. Try BYJU‘S free classes today!

34 & 46

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

37 & 50

No worries! We‘ve got your back. Try BYJU‘S free classes today!

51 & 46

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $34 & 46$
$F o r c o n t i n u o u s d a t a, m e d i a n = L + (\frac{\frac{N}{2} - C}{f}) \times H W h e r e N = T o t a l c u m u l a t i v e f r e q u e n c y L = l o w e r l i m i t o f t h e m e d i a n c l a s s I n t e r v a l; M e d i a n C l a s s = t h e c l a s s i n t e r v a l$
$h a v i n g c u m u l a t i v e f r e q \geq \frac{N}{2} l i e s C = c u m u l a t i v e f r e q u e n c y o f t h e c l a s s i n t e r v a l j u s t b e f o r e t h e m e d i a n c l a s s i n t e r v a l f = f r e q u e n c y o f t h e m e d i a n c l a s s i n t e r v a l; H = w i d t h o f t h e m e d i a n c l a s s$
$i n t e r v a l H e r e g i v e n N = 230 & f r o m t a b l e N = f_{1} + f_{2} + 150 G i v e n m e d i a n = 46, t h i s c u m u l a t i v e f r e q l i e s w i t h i n i n t e r v a l (40 - 50); \frac{N}{2} = 115, L = 40; C = f_{1} + 42; f = 65; H = 10 T h e r e f o r e 40 + (\frac{115 - (f_{1} + 42)}{65} \times 10) = 46 \Rightarrow (\frac{115 - 42 - f_{1}}{65} \times 10) = 46 - 40 \Rightarrow (73 - f_{1}) \times 10 = 6 \times 65 \Rightarrow 730 - 10 f_{1} = 390 \Rightarrow - 10 f_{1} = 390 - 730 \Rightarrow 10 f 1 = 340 \Rightarrow f_{1} = 34 N o w f_{1} + f_{2} + 150 = 230 \Rightarrow f_{2} = 230 - 150 - 34 \Rightarrow f_{2} = 46$

Suggest Corrections

Similar questions

46

46

Variable	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	Total
Frequency	$12$	$30$	$f_{1}$	$65$	$f_{2}$	$25$	$18$	$229$

Variable	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$12$	$30$	$-$	$65$	$-$	$25$	$18$

46

230.

Variable	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$12$	$30$	$x$	$65$	$y$	$25$	$18$

46

230

Variable:	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Frequency:	12	30	−	65	−	25	18

Join BYJU'S Learning Program