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Chapter 2: Measures of Central Tendency
Notes:
When computing the value of the median, the data values can be
population values or sample values.
Hence we can compute either the population median or the sample
median.
Both population and sample data values are assumed to be finite.
Definition: Median
The median of a set of numerical (data) values is the numerical value in the
middle when the data set is arranged in order.
Notes:
When the number of values in the data set is odd, the median will be
the middle value in the ordered array.
When the number of values in the data set is even, the median will be
the average of the two middle values in the ordered array.
Example 2-3:
What is the median for the following sample values?
3, 8, 6, 14, 0, -4, 2, 12, -7, -1, -10
Solution:
First of all, we need to arrange the data set in order. The ordered
set is given below. Note that the ordering is from the smallest value to the
largest value.
-10, -7, -4, -1, 0, 2, 3, 6, 8, 12, 14
Since the number of values is
odd
, then the median will be the middle value
in the ordered set. Thus, the median will be found in the 6
th
position since
we have a total of eleven values.
That is, the value of median is 2. This is demonstrated in
Figure 2-7
.