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Maths & statistic

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?

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  • R mwila Dec 13, 2008

    compute the quatile deviation

    compute the standard deviation

    compute the co-efficient of variation

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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.

Posted on Feb 08, 2008

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Hello,
I am happy that you found my solution helpful and even flattered that you copied it in this thread. By doing this, you gave me the opportunity to discover an error in my post. In fact, the calculator does provide a column for the frequency. If you enter nothing in the frequency column, all data items will have their frequency set to 1, by default.

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As my motto says, I am always happy to help, but happier still when people show true appreciation.

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Please rate this response . .

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Hello,

In the main menu select [STAT] icon to enter Stat mode and display the statistical data lists. Use the satistical data lists to input data and perform statistical calculations. Use the arrows to move the highlighting around the lists.
Exemple: Enter the following values in List 1
1st line enter 90 [EXE]
2nd line 85 [EXE]
3 79 [EXE]
4 75 [EXE]
5 70 [EXE]
6 68 [EXE]
7 56 [EXE]

When finished you press [F2:Calc], then [F1:1Var] and the statistical results appear on screen.
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x bar =74.7142857
Capital Sigma x= 523
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Scroll down with Down arrow to access other data
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All you have to do now, is to look at the theory you learned and interpret what these values mean.

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