Calculate mean of the following series:

Size : 4 5 6 7 8 9 10

Frequency : 6 12 15 28 20 14 5

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Solution

X f fX

4
5
6
7
8
9
10 6
12
15
28
20
14
5 24
60
90
196
160
126
50

Σf = 100 ΣfX = 706

$X = \frac{Σ f X}{Σ f} = \frac{706}{100} = 7.06$

Thus, mean of the series is 7.06.

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Values	:	60	62	64	67	70	73	77	81	85	89
Frequency	:	54	82	103	176	212	180	115	78	50	21

Mid-value	10	12	14	16	18	20
Frequency	5	8	12	20	10	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

Calculate the mean for the following frequency distribution using direct method.

$\begin{matrix} C l a s s & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 f_{i} & 6 & 8 & 20 & 25 & 15 & 10 & 4 \end{matrix}$

X	:	1	2	3	4	5	6	7	8	9	10
f	:	2	5	8	16	21	18	13	10	4	3

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