The median is the middle value in a data set arranged in numerical order. It represents the center of the data and is less affected by outliers than the mean. To calculate the median, the data is lined up from highest to lowest and the middle value is identified. For an even number of values, the median is the average of the two middle values. The document provides an example of how outliers can significantly impact the mean but not the median of a classroom test score data set.

1. MEDIAN

2. median, is the middle score in the
distribution when the numbers have
been arranged into numerical order,
from either highest to lowest or lowest
to highest. Like the mean, the median
is a numerical representation of the
center of the data set, and can be
used with interval or ratio data. The
median can also be used for ordinal
data

3.  To find the median, one lines up the scores
from highest to lowest (or lowest to highest)
and simply finds the middle score. If there is
an odd number of scores, the median is the
middle number of the lined up data set. If
there is an even number of scores, the
median is found by averaging the two middle
numbers (adding them up and dividing by
two) and that average is the median for the
data.

4.  Unlike the mean, extreme scores in the data
set, called outliers, have less of an effect on
the median. When outliers are present, the
mean is “pulled” in the direction of the
outlier, meaning an extremely high score
would result in a higher mean than if the
outlier was not present. The median on the
other hand, would be less affected by the
outlier, often resulting in little or no change
in the median.

5. The effect of outliers will be more
apparent when examining data
graphs in the distribution shape
(skew) section.

6. Example:
Mr. Frank wanted to compute the
median of the 15 scores from his
class. After lining up the scores, Mr.
Frank found the middle number,
which is the median of the scores:

7.  Example with Outliers:
 Let’s say though the next day three new students were
added to Mr. Frank’s class. He decided to test them
too. Their scores, which he added to the total
distribution, were: 10, 11, and 46. Since two of the new
scores appeared to be extremely different than the
rest of the scores Mr. Frank wanted to recalculate the
mean and median of his data. Now the mean looked a
little different:

8. Mr. Frank also recalculated the median after
adding the new scores to the data set.

9. Since there was an even number Mr. Frank
added the two middle numbers and divided by
two:

10. Note how the addition of the outliers
affects the mean and median. The
mean is greatly affected changing
from 46 to 42, which is no longer the
best representation of the center of
the data set. The median, on the other
hand, was unaffected by the outliers
and remained at 46.