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We can use the median along with the minimum and maximum to describe variation in data. The median divides the raisin-count data into two groups: the data values below the median and the data values above the median. Note that each group has eight data values, which is approximately half the data. Consequently, approximately half of the raisin-counts are in the interval 25 to 28 (from the minimum to the median), and approximately half of the raisin counts are in the interval 28 to 31 (from the median to the maximum).
We can also determine the median by looking at a line plot. For the line plot of the raisin counts, you can identify the 17 positions in the ordered data as follows:
Alternatively, you could number the 17 positions in this way:
These two line plots are identical, since there is no need to distinguish the order of raisin boxes that have the same number of raisins.
Again we see that the ordered lists contain 17 data values, and there are 17 positions in the ordered list. Position 9 contains the middle value because eight positions precede Position 9, and eight positions follow Position 9. Position 9 corresponds to a box that contains 28 raisins, so 28 is the median. This can be determined from either of the line plots above.
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