Who's the tallest of them all?
Five children in the same room have different heights in cm. as followed: , , , , .
What is the variance of heights among these five children?
The answer is 12.
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1 solution
The mean height of the five children = 5 1 2 1 + 1 2 3 + 1 2 7 + 1 2 9 + 1 3 0 = 1 2 6 .
The variance of heights = ∑ ( N ( x − μ ) 2 )
Then
∑ ( 5 ( x − 1 2 6 ) 2 ) = 5 ( 1 2 1 − 1 2 6 ) 2 + ( 1 2 3 − 1 2 6 ) 2 + ( 1 2 7 − 1 2 6 ) 2 + ( 1 2 9 − 1 2 6 ) 2 + ( 1 3 0 − 1 2 6 ) 2 )
= 5 5 2 + 3 2 + 1 2 + 3 2 + 4 2 = 5 6 0 = 1 2 .