Basics Statistics
Tuesday, 6 December 2011
Sunday, 4 December 2011
Arithmetic Mean (ungroup data & group data)
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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