Using assumed mean method find the mean weight of $40$ students using the data given below.
Weights in $k g$ . $50$ $52$ $53$ $55$ $57$
No. of students $10$ $15$ $5$ $6$ $4$

Open in App

Solution

$w_{i}$

$f_{i}$

Deviation
$d_{i} = (w_{i} - 53)$

$(u_{i} = \frac{d_{i}}{h})$

$u_{i} f_{i}$

50

10

-3

-1.5

-15

52

15

-1

-0.5

-7.5

53

5

0

0

0

55

6

2

1

6

57

4

4

2

8

$\sum f_{i} = 40$

$\sum u_{i} f_{i} = - 8.5$

N= $\sum f_{i} = 40$
A= $53$ ,h= $2$ , $d_{i} = w_{i} - A$ , $u_{i} = \frac{d_{i}}{h}$
Mean = $A + h (\frac{1}{n} \sum u_{i} f_{i}) = 53 + 2 (\frac{- 8.5}{40}) = 53 - 0.425$
Mean= $52.575$ kg

Suggest Corrections

Similar questions

Q. Calculate the arithmetic mean by assumed mean method for the data given below.

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
No. of students	$5$	$10$	$25$	$30$	$20$	$10$

Q. The mean weight per student in a group of seven students is 55 kg if the individual weights of 6 students are 52, 58, 55, 53, 56 and 54; then weight of the seventh student is

Calculate the Mean of the distribution given using Assumed mean Method.

$\begin{matrix} Marks & No. of Students 10 - 20 & 2 20 - 30 & 6 30 - 40 & 10 40 - 50 & 12 50 - 60 & 9 60 - 70 & 8 70 - 80 & 4 80 - 90 & 3 \end{matrix}$

Q. Below is given the distribution of money (in Rs.) collected by students for flood, relief fund

Money (in Rs)	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$ $	40-50$
No. of Students	$5$	$7$	$5$	$2$	$6$

Find mean of money (in Rs) collected by a student using 'Direct Method'.

Q. Calculate the arithmetic mean for the following data using step deviation method.

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
No. of students	$8$	$15$	$22$	$20$	$10$	$5$

Join BYJU'S Learning Program

Weights in $k g$ .	$50$	$52$	$53$	$55$	$57$
No. of students	$10$	$15$	$5$	$6$	$4$

$w_{i}$	$f_{i}$	Deviation $d_{i} = (w_{i} - 53)$	$(u_{i} = \frac{d_{i}}{h})$	$u_{i} f_{i}$
50	10	-3	-1.5	-15
52	15	-1	-0.5	-7.5
53	5	0	0	0
55	6	2	1	6
57	4	4	2	8
	$\sum f_{i} = 40$			$\sum u_{i} f_{i} = - 8.5$

Using assumed mean method find the mean weight of 40 students using the data given below.Weights in kg.5052535557No. of students1015564

wi fi Deviationdi=(wi−53) (ui=dih) uifi 50 10 -3 -1.5 -15 52 15 -1 -0.5 -7.5 53 5 0 0 0 55 6 2 1 6 57 4 4 2 8 ∑fi=40 ∑uifi=−8.5 N=∑fi=40A=53,h=2,di=wi−A,ui=dihMean =A+h(1n∑uifi)=53+2(−8.540)=53−0.425Mean=52.575kg

Using assumed mean method find the mean weight of $40$ students using the data given below.
Weights in $k g$ . $50$ $52$ $53$ $55$ $57$
No. of students $10$ $15$ $5$ $6$ $4$