Find an estimate of the combined variance of the following data for the marks obtained in a test by 88 students.
Marks (x) $0 \leq x < 10$ $10 \leq x < 20$ $20 \leq x < 30$ $30 \leq x < 40$ $40 \leq x < 50$
Frequency (f) 6 16 24 25 17

338.73

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

184.73

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

138.73

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

None of these

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

Open in App

Solution

The correct option is D $138.73$

$x$

0-10

10-20

20-30

30-40

40-50

$f$

6

16

24

25

17

Mid point $(m_{i})$

5

15

25

35

45

Mean $= ¯ X = \frac{\sum m . f}{\sum f} = 28.52$

Variance $= σ^{2} = \frac{\sum (¯ X - m_{i})^{2} f}{\sum f} = \frac{12208.15}{88} \approx 138.73$

Suggest Corrections

Similar questions

Marks (x)	$0 \leq x < 10$	$10 \leq x < 20$	$20 \leq x < 30$	$30 \leq x < 40$	$40 \leq x < 50$
Frequancy (f)	6	16	24	25	17

50

Marks obtained	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
No. of students	$5$	$12$	$20$	$10$	$3$

x

y

31

$C I$	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	Total
Frequency	$5$	$x$	$6$	$y$	$6$	$5$	$40$

25.2

x

$C . I .$	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
frequency	$8$	$X$	$10$	$11$	$9$

31.4

x

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
Frequency	$5$	$x$	$10$	$12$	$7$	$8$

Join BYJU'S Learning Program