Sheet1
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Historical data
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Random variable data
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Prob
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X
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(X-avg)^2
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(p)
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X
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pX
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X^2
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p(X^2)
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4.0
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4.0
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20%
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4.0
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0.8
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16.0
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3.2
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5.0
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1.0
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20%
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5.0
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1.0
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25.0
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5.0
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7.0
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1.0
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20%
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7.0
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1.4
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49.0
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9.8
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6.0
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0.0
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20%
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6.0
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1.2
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36.0
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7.2
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8.0
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4.0
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20%
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8.0
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1.6
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64.0
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12.8
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Population variance
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Random variable variance
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average
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6.0
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2.0
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sum
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100%
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6
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38
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formula
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2.0
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E(X^2)-[E(X)]^2
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2.0
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Sample variance
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average
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2.5
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formula
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2.5
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Sheet2
Sheet3
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