#### Arithmetic Means

If the total sum observation is divided by a total number of observations, then it is called arithmetic mean. It is denoted by $$\overline{X}$$ (Read as X-bar)
∴ Arithmetic Mean = $$\frac{Total\;sum\;of\;observation}{Total\;no.\;of\;observation}$$
For example,
Arithmetic mean of 1, 3, 7, 11, & 13

= $$\frac{1+3+7+11+13}{5}$$
= $$\frac{35}{5}$$
= 7

1. Calculation of Mean for individual series
The mean of individual series is calculated by adding all the observation and dividing the sum by the total number of observation.
If x1, x2, x3, …………..xn are be n variants value of variable a. Then arithmetic mean is denoted by
$$\overline{X}$$ = $$\frac{x_1+ x_2+ x_3+ …………..x_n}{n}$$ = $$\frac{∑X}{n}$$
Where ∑X = sum of n observation or items
n = no. of observations or items.
X = variable.

2. Calculation of Mean for discrete series
Mean for discrete series can be calculated by Mean $$\overline{X} = \frac{sum\;of\;the\;product\;of\;f\;and\;x}{sum\;of\;f}$$
= $$\frac{∑fx}{N}$$

3. Calculation of Mean for continuous series
For calculating mean in continuous series the following formulae is used:
$$\overline{X}$$ = $$\frac{∑fx}{N}$$ where, F = Frequency and m = mid-value.

• If the total sum observation is divided by total number of observations, then it is called arithmetic mean. It is denoted by $$\overline{X}$$.
• The mean of individual series is calculated by adding all the observation and dividing the sum by the total number of observation.
0%

1
9
5
6

-5
-7
-6
2

12
16
5
8

25.02
21.6
46
20

-6
2
-1
3

5
4
9
6

41
26
25
12

4
2
56
12

21
25
36
45

15
20
25
14

20
18
26
12

45
60
80
55

12
13
12.33
14

14
15
16
12

25
5
15
20