Question

Find the mean by direct method:

Class interval	0 – 8	8 – 16	16 – 24	24 – 32	32 – 40
Frequency	8	10	15	9	8

Answer 1

Step 1: Calculate midpoints (x_i) and product (f_ix_i)

The midpoint x_i is calculated as:

`x_i = ("Lower Limit" + "Upper Limit")/2`

Class Interval	Frequency (fi)	Midpoint (xi)	fi × xi
0 – 8	8	4	32
8 – 16	10	12	120
16 – 24	15	20	300
24 – 32	9	28	252
32 – 40	8	36	288
Total	Σfi = 50		Σfixi = 992

Step 2: Apply the mean formula

The formula for the mean `(barx)` using the direct method is:

`barx = (sumf_ix_i)/(sumf_i)`

Substituting the values from our table:

`barx = 992/50`

`barx = 19.84`

The mean for the given data is 19.84.