## Data Visualization And Data Analytics

#### GET ASSIGNMENT HELP # 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; 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

n

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:

 Variable xi Frequency fi fixi di = (xi – x ) di2 fi di2 2 4 6 8 10 12 14 16 4 4 5 15 8 5 4 5 8 16 30 120 80 60 56 80 -7 -5 -3 -1 1 3 5 7 49 25 9 1 1 9 25 49 196 100 45 15 8 45 100 245 Σ fi = 50 Σfixi = 450 Σfi di2 = 754

### 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 49 36 0 1 4 49 196 225 144 49 72 0 1 4 49 196 -15 -12 -7 -12 0 1 2 7 14 Σfi = 10 Σ fidi2 = 740 Σfidi = -22

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