Question and Answer

Quiz - 5

A data set is given

548 326 854 865 933

Find the Mean, Variance, and Standard Deviation of the Data

  • Mean: 705.2
  • (Population)Variance: 53614.96
  • (Population)Standard Deviation: 231.549

To find mean, one simply adds the given values and then divides the sum by the number of values
In this case: 548 + 326 + 854 + 865 + 933 = 3526 ; 3526/5 = 705.2

It takes a few steps to find variance. One begins by finding how far from the mean each data point lies
In this case: 548-705.2=-157.2 326-705.2=-379.2 854-705.2=148.8 865-705.2=159.8 933-705.2=287.8

Then one proceeds to take the average of the squared values of these numbers
In this case: (-157.2)^2 + (-379.2)^2 + (148.8)^2 + (159.8)^2 + (287.8)^2 = 268074.8 ; 268074.8/5 = 53614.96

To find the Standard Deviation, you then simply take the square root of the Variance
In this case: sqrt(53614.96) = 231.549

- Adrian M. Guerrero

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