Variance Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Calculate the population variance for: {1,3,5,7,9}\{1, 3, 5, 7, 9\}.

Solution

  1. 1
    Mean: ฮผ=(1+3+5+7+9)/5=25/5=5\mu = (1+3+5+7+9)/5 = 25/5 = 5
  2. 2
    Squared deviations: (1โˆ’5)2=16,ย (3โˆ’5)2=4,ย (5โˆ’5)2=0,ย (7โˆ’5)2=4,ย (9โˆ’5)2=16(1-5)^2=16,\ (3-5)^2=4,\ (5-5)^2=0,\ (7-5)^2=4,\ (9-5)^2=16; Sum =40= 40
  3. 3
    Variance: ฯƒ2=40/5=8\sigma^2 = 40/5 = 8

Answer

ฯƒ2=8\sigma^2 = 8
The population variance formula ฯƒ2=โˆ‘(xiโˆ’ฮผ)2n\sigma^2 = \frac{\sum(x_i - \mu)^2}{n} divides by nn for a complete population. The result of 8 indicates moderate spread around the mean of 5.

About Variance

The variance is the average of the squared deviations from the mean: ฯƒ2=1nโˆ‘(xiโˆ’xห‰)2\sigma^2 = \frac{1}{n}\sum (x_i - \bar{x})^2. It is the square of the standard deviation.

Learn more about Variance โ†’

More Variance Examples

Example 1 medium

Calculate the population variance for the data set: [formula].

Example 2 hard

Two investments have the same mean return of 8%. Investment A returns: [formula]. Investment B retur

Example 4 medium

A data set has [formula] values with mean [formula] and [formula]. Find the variance using the compu

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