Examples on how to find the mean, median and mode of a data set of real
numbers are presented along with their detailed solutions and explanations.
The mean, median and mode are statistical measures of central tendencies
that in a well distributed data tends to summarize a whole data set with a
single value. These three measures are easy to understand and to use in
comparing data sets.
The outliers are also defined and discussed and their effects on the mean,
median and mode discussed through examples with their solutions.
Online calculators to compute the Mean , the Median and the Mode are
included.
Mean of a Data Set
x1, x2, x3 ... xN are the values in a data set, the mean μ is given by the
formula
Example 1
In a math exam, the students in class A scored 55, 72, 96, 92, 87, 52,
92, 45, 58, 77, 86, 80 and the students in class B scored 55, 67, 75 ,
95, 82, 86, 38, 90, 42, 56, 82, 96. What is the mean (average) score of
each class? Use the two means to compare the performance of the
two classes.
Solution to Example 1
There are 12 scores in class A hence N = 12. Use the formula to
calculate the mean for class A as follows
There are 12 scores in class B hence N = 12. Use the formula to
calculate the mean for class B as follows
The mean (average) of class A is higher that the mean of class B. On
average, class A "scored" better than class B, but If we examine the
two sets of scores, not all students in class A scored higher than all
students in class B.
For any given data set of values, the mean is larger that the smallest
value and smaller that the largest value. In class A above the smallest
score is 55 and the largest score is 96 and the mean is 74.3. In class
B, the mean is 72 and the smallest and largest scores are 55 and 96
respectively.
Median of a Data Set
The median of a data set is the middle data value after ordering the
given data. If the number N of data values is odd, the median is the
middle data vale and if N is even, the median is the average of the two
data values in the middle.
Example 2
The heights, in centimeters, of a group of 11 children of different ages
are follows: 110, 105, 126, 65, 134, 102, 78, 80, 119, 67, 88. What is
the median height of this group of children?
Solution to Example 2
We first order the given data from smallest to the largest hei