Question

Consider the following population data values

22        16     -7    10   39     -13

a) Calculate the range.

​b) Calculate the variance.

​c) Calculate the standard deviation.

Answer 1

(a) Range = Largest value - Smallest Value = 39 - (13) = 39 + 13 = 52

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(b) Variance = Sum of Squares / n

Where Sum of squares = (X - Mean)².

Mean = 11.17

Therefore Variance = [(22 - 11.17)² + (16 - 11.17)² + (-7 - 11.17)² + (39 - 11.17)² + (10 - 11.17)² + (-13 - 11.17)² ] / 6

= 1830.83 / 6

Variance = 305.14

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(c) Standard Deviation = Sqrt(Variance) = Sqrt(305.14) = 17.47

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