1. Three young boys have total age of 24. Answer the following questions with proper calculation steps and explanation.
If standard deviation of these boys’ ages is 0, what is the age of the oldest boy of the three?
Standard deviation is the average root mean squared deviation from the average of the numbers.
Familiarize yourself with the wikipedia page on standard deviation: http://en.wikipedia.org/wiki/Standard_deviation
In this case, your question is easy. The standard deviation is 0, so this means the boys ages are all the same.
So they're all 24/3 = 8 years old.
Proof:
8 + 8 + 8 = 24 <-- satisfies the constraint that the boys ages must total to 24.
Get the standard deviation of these numbers;
8+8+8 / 3 = 8 <-- the average value is 8
The deviation of each boy's age from the average is:
boy 1
--------
8 years old, which deviates from 8 by 0
boy 2
--------
8 years old, which deviates from 8 by 0
boy 3
--------
8 years old, which deviates from 8 by 0
So the deviations are 0, 0 and 0.
To get the standard deviation, you sum the squares of the deviations of each boy, get the average, and square root. So:
0² + 0² + 0² = 0
Average is 0 / 3 = 0
Square root of 0 = 0
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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