How to calculate central value of the following sets: I'm thinking is the same as the median - is it?
$\{-2, -1, 3, 5, 7 , 1, 3 , 6, 2 , -1, -5\}$ and $\{-2, -1, 3, 5, 7 , 1, 3 , 6, 2 , -1 \}$
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Probably the median. What else can it be? – Shahar Apr 16 '14 at 00:07
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The term "central value" is ambiguous. This link may help, but without some other information, there's no way to know whether you're supposed to find the arithmetic mean, median, mode, or some other measure of central tendency.
This is what people most frequently mean when they say "average." You can calculate the arithmetic mean of a collection of numbers by dividing their sum by the number of numbers. For the set $\left\{ -2, -1, 3, 5, 7 , 1, 3 , 6, 2 , -1, -5\right\}$, the sum is $18$ and there are $11$ elements, so the average is $$\frac{18}{11} \approx 1.636$$
For the set $\left\{ -2, -1, 3, 5, 7 , 1, 3 , 6, 2 , -1 \right\}$, the sum is $23$ and there are $10$ numbers, so the average is $$\frac{23}{10} = 2.3$$
Intuitively, this is the "middle" number of a set of numbers, if they are put in increasing (or decreasing) order. The median of set $\{-2, -1, 3, 5, 7 , 1, 3 , 6, 2 , -1, -5\}$ is $2$. The median of the set $\{-2, -1, 3, 5, 7 , 1, 3 , 6, 2 , -1\}$ is between $2$ and $3$, so it is equal to $$\frac{2+3}{2}=2.5$$
This is simply the most frequently occurring number, or, in the case of a tie, there can be more than one mode. Both of your sets have two modes: $3$ and $-1$.
Zubin Mukerjee
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