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

11.78

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

24.53

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

14.76

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

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 11.78
Mid point of given data
Mid point $(m_{i})$
5
15
25
35
45
Mean $= ¯ X = \frac{\sum m . f}{\sum f} = 28.52$
Standard deviation $= \frac{\sum (¯ X - m_{i})^{2} f}{\sum f} = \frac{12208.15}{88} = \sqrt{138.73} = 11.78$

Suggest Corrections

Similar questions

Marks (x)	$0 \leq x < 10$	$10 \leq x < 20$	$20 \leq x < 30$	$30 \leq x < 40$	$40 \leq x < 50$
Frequency (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	$5$	$x$	$6$	$y$	$6$	$5$	$40$

:

X	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
F	$20$	$10$	$10$	$10$	$40$	$30$

$x$	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
$f$	$5$	$8$	$15$	$16$	$6$

Join BYJU'S Learning Program