Median from a frequency table
The median is the “middle” value from an ordered list. It is often preferred to the mean (the average) due to the fact that the mean may skew the results. For example, if 8 players deposit 5 each but 1 player deposits 1000, the mean would be the following,
This means that the average deposit for all 9 players is 115.55 euros. This does not make sense when considering that one of these is an outlier (the 1000 deposit).
The mode is the highest value in the list, which is 1000.
The median, on the other hand, picks the middle item in the ordered list. Thus, first we list all of the items in the list in order:
And then we pick the middle item, which is 5.
This is pretty simple. The problem occurs when we need to find the median from a frequency table. Let us take the following example.
Suppose we are opening a summer class for anyone between the ages of 14 and 18 and we draw up the table below with the number of applicants in each age range.
The mean can simply be calculated by adding all of the numbers and dividing by the number of age groups.
The mode is the highest value, which is 3.
The median is calculated by considering the middle value which can be found as,
