5.4. Median http://www.ck12.org
When data is entered into a frequency table, a column that displays thecumulative frequencyis often included.
This column is simply the sum of the frequencies up to and including that frequency. The median can be determined
by using the information that is presented in the cumulative frequency column.
In this example, there are 26 data values, which is an even number. The middle position isn+ 21 =^262 +^1 =^272 = 13 .5,
and the median is the sum of the numbers above and below position 13.5 divided by 2. According to the table, the
numbers in the 13thand 14thpositions are 2’s. Therefore, the median is^2 + 22 =^42 =2 goals.
Points to Consider
- The median of a set of data values cuts the data in half. Is only the median of an entire set of data a useful
value? - Is the median of a set of data useful in any other aspect of statistics?
- Other than as a numerical value, can the median be used to represent data in any other way?
Guided Practice
The students from a local high school volunteered to clean up the playground as an act of community service. The
numbers of pop cans collected by 20 of the students are shown in the following table: