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Algebra I: Median |
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Median is a measure of central tendency commonly
used in statistics and probability.
It is a value in the middle of the distribution, dividing
the distribution in such a way that there are an equal number of values above and
below it.
In order to find the median for a set of ungrouped values, first, the N
values should
be ordered in an increasing order. If N is odd, the value at the position (N+1)/2
is the median value. If N is even, the median is the average of the two values at
the positions N/2 and N/2
+ 1.
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Example:
Find the median for the following
list of values: 10, 8, 11, 10,
12, 10, 11, 9, 13
Solution: Median is the middle value, so rewrite the list in ascending order:
8, 9, 10, 10, 10, 11, 11, 12, 13
There are nine numbers in the list, so the middle one will be the (9 + 1)/2 = 10/2 = 5th number.
Therefore, median is 10.
Example: Find the median for the following list of values: 13, 18, 14, 13, 13, 16, 14, 21
Solution: First rewrite the list in ascending order:
13, 13, 13, 14, 14, 16, 18, 21.
There are eight numbers in the list, so the middle one will be the (8 + 1)/2 = 9/2
= 4.5th number.
So the median will be the average of 4th and 5th number i.e. (14 + 14)/2 = 14.
Therefore, median is 14.
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