Math Assignment Help With Variance and Standard Deviation

10.3.2 Variance and Standard Deviation:

The variance is the measure of variability about the mean and is symbolized by "σ²”

The square root of variance is called the standard deviation. It is represented by σ.

10.3.2.1 Methods of finding variance and standard deviation:

Case I : when each term has frequency 1

Let x1 x2……xn are the n given observations and let x be their mean. Then the variance is given by;

$methods of finding variance and standard deviation$

Variable xi	Deviation from the mean di = (xi – x )	di²
10 11 8 15 16	10 – 12 = -2 11 – 12 = -1 8 – 12 = -4 15 – 12 = 3 16 – 12 = 4	4 1 16 9 16
		Σdi² = 46

Therefore,

Variance = σ2 = Σdi2 = 46/5 = 9.2

and standard deviation = σ = √9.2 = 3.303

Case II: When the frequencies of the variable are given. The variance is given by

σ² = Σ fi di² & S.D = σ = Σ fi di²

Σf i Σf i

Example: find the variance and standard deviation from the given distribution table.

Variable (xi)	2	4	6	10	12
Frequency (fi)	4	4	5	5	6

Solution:

Example: The scores of 10 students in an examination, in which maximum marks were 50 is given. Find the variance?

Variable
xi

Frequency
fi

di = xi – A

di²

fidi²

fidi

19
22
27
28
34
35
36
41
48

1
1
1
2
1
1
1
1
1

-15
-12
-7
-6
0
1
2
7
14

225
144

196

225

144

196

-15

-12

-7

-12

Σfi = 10

Σ fidi² = 740

Σfidi = -22

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