Question

Find the mean of the following data using assumed mean method:

Class	0 – 5	5 – 10	10 – 15	15 – 20	20 – 25
Frequency	8	7	10	13	12

Answer 1

Let us first construct the table for d_i × f_i,

where d_i = x_i – A (Assumed mean), as shown below:

Class	Class Marks `("x"_"i")`	Frequency `("f"_"i")`	`"d"_"i" = "x"_"i" - "A"`	`"d"_"i" xx "f"_"i"`
0 – 5	2.5	8	– 10	– 80
5 – 10	7.5	7	– 5	– 35
10 – 15	12.5 = A	10	0	0
15 – 20	17.5	13	5	65
20 – 25	22.5	12	10	120
		`sum"f"_"i" = 50`		`sum"f"_"i" "d"_"i" = 70`

Let A = 12.5,

Then `sum"f"_"i" "d"_"i"` = 70

Now, the required mean

`(bar"x") = "A" + (sum"f"_"i" "d"_"i")/(sum"f"_"i")`

= `12.5 + 70/50`

= 12.5 + 1.4

= 13.9