Find the mean of the following frequency distribution:
Marks obtained Number of students
10-20 $6$
20-30 $8$
30-40 $13$
40-50 $7$
50-60 $3$
60-70 $2$
70-80 $1$

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Solution

Let assumed mean $A = 45$
and interval $i = 10$
Marks No. of students Mid value $u = \frac{x - A}{i}$ $f \times u$
10-20 6 15 -3 -18 -47
20-30 8 25 -2 -16
30-40 13 35 -1 -13
40-50 7 45 0 0
50-60 3 55 1 3 10
60-70 2 65 2 4
70-08 1 75 3 3
Total $\sum f = 40$ $\sum f = - 37$

Formula Mean $= A + \frac{\sum f u}{\sum f} \times i$

$= 45 + \frac{- 37}{40} \times 10 = 45 - \frac{37}{4} = 45 - 9.25 = 35.75$

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Similar questions

Marks	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$3$	$7$	$10$	$6$	$8$	$2$	$4$

Marks obtained	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Number of Students	$6$	$8$	$13$	$7$	$4$	$2$

Class	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$2$	$3$	$8$	$14$	$8$	$3$	$2$

Class Interval	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$10$	$6$	$8$	$12$	$5$	$9$

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$5$	$8$	$7$	$12$	$28$	$20$	$10$	$10$

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