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Find the variance of the following data.

Observations 1 2 3 4 5 6 7
Value 25 26 38 45 31 30 29

 


1. 50.7
2. 51.7
3. 57
4. 50

1 Answer

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Best answer
Correct Answer - Option 1 : 50.7

Concept:

Sample Variance:

  • Sample variance (s2) is a measure of the degree to which the numbers in a list are spread out.
  • If the numbers in a list are all close to the expected values, the variance will be small.
  • If they are far away, the variance will be large.

Sample variance of n observations is given by

\(s^2\ =\ \frac{1}{n-1}∑ (x_i\ -\ ̅{x})^2\)

Where is the sample mean and given by

\(̅{x}\ =\ \frac{∑ x_i}{n}\ =\ \frac{x_1+x_2=\dots x_n}{n}\)

Calculation:

Here, ∑x = 224  and n = 7

Using the formula of sample mean, we will get

x̅ = 224/7 = 32

Observation Value (xi - x̅)2 
1 25 49
2 26 36
3 38 36
4 45 169
5 31 1
6 30 4
7 29 9
n = 7 ∑x = 224  ∑(xi - x̅)2 = 304 

 

Therefore, sample variance

\(s^2\ =\ \frac{1}{n-1}∑ (x_i\ -\ ̅{x})^2\)

\(\Rightarrow\ s^2\ =\ \frac{1}{7-1}(304)\ =\ 50.7\)

Hence, option 1 is correct.

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