Find out arithmetic mean from the following distribution by Short-cut Method:

Items 10−8 8−6 6−4 4−2 2−0

Frequency 10 8 6 4 2

Open in App

Solution

Items
(X) Mid-Values
(m) Frequency
(f) Deviation
m − A
(d) fd

0 − 2
2 − 4
4 − 6
6 − 8
8 − 10 1
3
5 = A
7
9 2
4
6
8
10 −4
−2
0
2
4 −8
−8
0
16
40

∑f = 30 ∑fd = 40

Here, the assumed mean is decided from the mid-points. Let us take 5 as the assumed mean. So, we calculate the deviations of the mid-values from 5
$X = A + \frac{Σ f d}{Σ f} H e r e, A represents the assumed mean d represents the deviations of the mid - values from the assumed mean = 5 + \frac{40}{30} = 5 + 1.33 = 6.33$

Hence, the mean of the given distribution is 6.33

Suggest Corrections

Class Interval	10−20	20−40	40−70	70−120	120−200
Frequency	4	10	26	8	2

Size	0−4	4−6	6−10	10−15	15−20	20−30	30−35	35−40
Frequency	2	4	3	5	2	20	6	8

Class Interval	20−25	25−30	30−35	35−40	40−45	45−50	50−55
Frequency	10	12	8	20	11	4	5

Size of Items	3−4	4−5	5−6	6−7	7−8	8−9	9−10
Frequency	3	7	22	60	85	32	9

Age (in years)	18-24	24-30	30-36	36-42	42-48	48-54
Number of workers	6	8	12	8	4	2