Question

Find the mean by short-cut method:

Class	10 – 30	30 – 50	50 – 70	70 – 90	90 – 110
Frequency	90	20	30	20	40

Answer 1

First, let’s find the mid-points (x_i) and then choose an assumed mean A = 60 since it’s the middle value.

Class	Frequency (fi)	Class Mark (xi)	Deviation di = (xi – 60)	fidi
10 – 30	90	20	–40	–3600
30 – 50	20	40	–20	–400
50 – 70	30	60 (A)	0	0
70 – 90	20	80	20	400
90 – 110	40	100	40	1600
Total	Σfi = 200			Σfidi = –2000

Final calculation

Now, substitute the values into the formula:

1. Assumed mean (A): 60

2. Sum of frequencies (Σf_i): 200

3. Sum of f_id_i (Σf_id_i): –2000

`barx = 60 + ((-2000)/(200))`

`barx = 60 + (-10)`

`barx = 50`

The mean of the given data is 50.