What is the variance of the data? 0.0625 0.25 0.5 1.5

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MrRoyal MrRoyal · Answer 1 · 2022-04-25T12:42:12+02:00

The variance of the dataset is the square of their standard deviation

The variance of the dataset is 0.307

The dataset is given as;

0.0625 0.25 0.5 1.5

Calculate the mean using:

μ = Sum/Count

So, we have:

μ = (0.0625 + 0.25 + 0.5 + 1.5)/4

Evaluate

μ = 0.578125

The variance is then calculated using:

[tex]\sigma^2 = \frac{\sum(x - \mu)^2}{n}[/tex]

So, we have:

[tex]\sigma^2[/tex] = [(0.0625 - 0.578125)^2 + (0.25 - 0.5781250^2 + (0.5 - 0.578125)^2 + (1.5 - 0.578125)^2]/4

Evaluate

[tex]\sigma^2[/tex] = 1.2294921875/4

Divide

[tex]\sigma^2[/tex] = 0.30737304687

Approximate

[tex]\sigma^2[/tex] = 0.307

Hence, the variance of the dataset is 0.307