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\015 1. Three young boys have total age of 24. Answer the following questions with proper calculation steps and explanation.\015\012If standard deviation of these boys\342\200\231 ages is 0, what is the age of the oldest boy of the three? \015

## Answers :

\015\012

\015\012Familiarize yourself with the wikipedia page on standard deviation: http://en.wikipedia.org/wiki/Standard_deviation

\015\012

\015\012In this case, your question is easy. The standard deviation is 0, so this means the boys ages are all the same.

\015\012

\015\012So they're all 24/3 = 8 years old.

\015\012

\015\012Proof:

\015\012 8 + 8 + 8 = 24 <-- satisfies the constraint that the boys ages must total to 24.

\015\012

\015\012 Get the standard deviation of these numbers;

\015\012

\015\012 8+8+8 / 3 = 8 <-- the average value is 8

\015\012

\015\012 The deviation of each boy's age from the average is:

\015\012 boy 1

\015\012 --------

\015\012 8 years old, which deviates from 8 by 0

\015\012 boy 2

\015\012 --------

\015\012 8 years old, which deviates from 8 by 0

\015\012 boy 3

\015\012 --------

\015\012 8 years old, which deviates from 8 by 0

\015\012

\015\012 So the deviations are 0, 0 and 0.

\015\012

\015\012 To get the standard deviation, you sum the squares of the deviations of each boy, get the average, and square root. So:

\015\012

\015\012 0² + 0² + 0² = 0

\015\012 Average is 0 / 3 = 0

\015\012 Square root of 0 = 0

\015\012

\015\012 So the standard deviation is 0. Which shouldn't be much of a surprise to you. We just had to actually DO the work to show that it was in fact 0.

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