When summarizing a data set, we often want to produce a single number that best represents all numbers in the data set. One way to do this is to calculate the mean of the data set. Remember that the mean represents the "center" of the data set.
However, another way to find a single number that represents the center of a data set is to calculate the median.
To compute the median, we order the data points from smallest to greatest and find the number in the middle.
To demonstrate, let's compute the median of the data set below:
First, we order the data points from smallest to greatest:
Now, we find the middle data point:
Therefore, the median is
A school library has science books stored on five shelves. The number of books kept on each shelf is given below.
What is the median number of books on each shelf?
First, we order the data points from smallest to greatest:
Now, we find the middle data point:
So, the median of the data set is
Find the median of the following data set: \[ 11, \: 6, \: 8, \: 2, \: 14 \]
|
a
|
$7$ |
|
b
|
$10.5$ |
|
c
|
$9.2$ |
|
d
|
$9$ |
|
e
|
$8$ |
The weekly allowance that Jo gave to her son Tim is given below.
$\qquad$ $ \$ 10, \quad \$ 11, \quad\$ 10, \quad \$ 10, \quad \$ 12.$
Find Tim's median weekly allowance.
|
a
|
$\$10$ |
|
b
|
$\$12$ |
|
c
|
$\$21$ |
|
d
|
$\$20$ |
|
e
|
$\$11$ |
When a data set has an even number of data points, the data set does not have a single middle number. So, the median is computed as the mean of the two middle numbers.
For example, consider the following data set, which is already ordered from smallest to greatest:
Since our data set has an even number of data points (), the median is the mean of the two middle numbers:
Computing the mean of these two middle numbers gives
Therefore, the median of the data set is
Six children were playing a game with marbles. The children each had the following numbers of marbles in their pockets:
What is the median number of marbles each child had when the game started?
First, we order the data points from smallest to greatest:
Since our data set has an even number of data points (), the median is the mean of the two middle numbers:
So, the median of the data set is
Therefore, the median number of marbles is
Find the median of the following data set: \[ 2, \; 5, \; 8, \; 1, \; 2, \; 2 \]
|
a
|
$1$ |
|
b
|
$4$ |
|
c
|
$5$ |
|
d
|
$2$ |
|
e
|
$8$ |
Ten international students participated in a language test. The results obtained by each student are given below:
\[ 6, \, \, 7, \, \, 8, \, \, 7, \, \, 9, \, \, 6, \, \, 5, \, \, 8, \, \, 9, \, \, 9 \]
What is the median of the student's scores?
|
a
|
$8.5$ |
|
b
|
$8$ |
|
c
|
$7.5$ |
|
d
|
$5.5$ |
|
e
|
$6.5$ |