Description:
Mean-Median-Mode questions ask you to compute the mean, median and/or
mode for a given set of data. Mean equals average, median equals middle,
and mode equals most often.
Approach:
Make sure you rearrange the data from least to greatest when dealing with
a median question, and never
take the average of two averages when
solving for a mean.
1) Arithmetic Mean (Average)
The arithmetic mean of a set is synonymous with the average of the set.
In order to calculate the mean of a set, first add together the values of all
the members in the set to find the set's total. Then divide that total by the number of
members in the set.
For example:
What is the average (arithmetic mean) of 62, 44, and 86?
-
First add the three numbers together: 62 + 44 + 86 = 192
-
Then divide the total by 3 since there are three numbers in the set:
192 / 3 = 64
2) Median (Middle)
The term median refers to the middle number of a set that is arranged
in order (ascending or descending).
For example:
Given the set {3, 6, 8, 12, 14},
the median is 8.
If a set of numbers is not given in numerical order, you must first
reorganize them from least to greatest and then find the median.
For example:
What is the median of the following set:
{6, -2, 14, 36, 12}
-
First, arrange the numbers in order as follows:
{-2, 6, 12, 14, 36}
-
The median is the middle value, 12
Exception: When a set of numbers has an even number of members,
take the average of the two numbers in the middle to find the median.
For example:
What is the median of the following set:
{2, 7, 13, 15, 18, 20}
-
The average of the middle numbers is (13 + 15) / 2, or 14, so 14 is the
median.
3) Mode (Most Often)
The mode is the number that shows up the most times in a given set.
For example:
In the set {-3, -5, 2, 6, 2, 8, 2, 13}, the mode is 2
because it appears more than any of the others.
4) Practice:
-
Determine the mean, median and mode for the set {2, 9,
7, -3, 9, 6, 12}
-
Determine the median for the set {3,-4,6,8,-10, 15}
