__Defination:__ Arithmetic mean can be defined as:

The sum of all values in the series divided by the total numbers of values in the series.

The method of Arithmetic mean is also known as:

- Arithmetic mean

- Mean

- Simple mean

- Average

- Mean by direct method

**Arithmetic Mean (ungroup-data)**Formula:

Mean = sum of elements / number of elements

= a1+a2+a3+.....+an/n

Arithmetic Mean = ΣX/n

where

X = Individual value

n = Total number of values

**Example: To find the mean of 3,5,7.**

Step 1: Find the sum of the numbers.

3+5+7 = 15

Step 2: Calculate the total number.

there are 3 numbers.

Step 3: Finding mean.

15/3 = 5

**Ans = 5**

__:__

**Arithmetic Mean (group-data)**Formula:

Arithmetic Mean = ΣfX/Σf

where

X = Individual value

f = Frequency

Grouped Data Arithmetic Mean Example:.

X -Value Frequency(f) ΣfX

1 2 1 * 2 = 2

2 3 2 * 3 = 6

3 2 3 * 2 = 6

Σf = 7 ΣfX= 14

Step 1: Find Σf.

Σf = 7

Step 2: Now, find ΣfX.

ΣfX = 14

Step 3: Now, Substitute in the above formula given

Arithmetic mean = ΣfX/Σf = 14/7 = 2

Example:.

Classes Frequency

of Class

Age (years) f

0 --- 5 6

5 --- 10 12

10 ---15 19

15 ---20 3

Total

Find Arithmetic mean for given data.

As the formula for A.M (Group data) = ΣfX/Σf

So we need “X” first

Classes Frequency Mid Point

of Class

Age (years) f X fX

0 --- 5 6 2.5 15

5 --- 10 12 7.5 90

10 ---15 19 12.5 237.5

15 ---20 3 17.5 52.5

Total 40 395

Note: [In this example we have already class boundary, If class boundary not given to find A.M then no problem and we will not make class boundary. Class boundary is required only for Median, Mode, Quartile, Decile,

**Percentile**
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ReplyDeleteHow will we take the mid-point or the value of x, if the class boundary is not given?

ReplyDeleteto find-out the x, first we add the age limits and then divide by '2'.

ReplyDelete(0+5)/2=2.5 (5+10)/2=>15/2=7.5 .............

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