Yet another way to represent the center of a data set is to use the mode of the data. The mode is the value that occurs most often in the data set.
To demonstrate, let's compute the mode of the data set below:
Here, the number appears twice, while all the other numbers ( and ) each appear only once.
Therefore, the mode is
Note: Sometimes, there may be multiple values that occur most often in a data set. For example, in the data set below, the numbers and each appear twice.
In these cases, there are multiple modes in the data set. Here, there are two modes: and
What is the mode of the following data set?
Let's start by sorting our data set:
The mode is the value that occurs the most often in the data set. We have that:
appears time
appears times
appears times
appears times
The value appears more frequently than the others ( times in total).
Therefore, the mode is
Find the mode of the following data set: \[ 6, \; 6, \; 7, \; 7, \; 8, \; 8, \; 8, \; 9, \; 9 \]
|
a
|
$7$ |
|
b
|
$6$ |
|
c
|
$3$ |
|
d
|
$9$ |
|
e
|
$8$ |
Find the mode of the following data set:
\[ 5, \; 4, \; 5, \; 4, \; 5, \; 3 \]
|
a
|
$4$ |
|
b
|
$5$ |
|
c
|
$4.5$ |
|
d
|
$3$ |
|
e
|
$5.5$ |
Find the mode of the following data set:
Let's start by sorting our data set:
The mode is the value that occurs the most often in the data set. We have that:
appears time
appears times
appears times
appears time
The values and both appear more frequently than the others ( times each in total).
Therefore, the data set has two modes: and
Find the modes of the following data set:
\[ 1, \: 1, \: 1, \: 5, \: 6, \: 7, \: 7, \: 7, \: 8 \]
|
a
|
$7$ only |
|
b
|
$1$ and $7$ |
|
c
|
$5,$ $6,$ and $8$ |
|
d
|
$8$ only |
|
e
|
$1$ only |
Find the modes of the following data set:
\[ 6, \: 5, \: 4, \: 4, \: 5, \: 9, \: 3 \]
|
a
|
$4$ and $5$ |
|
b
|
$9$ only |
|
c
|
$4$ and $9$ |
|
d
|
$4$ only |
|
e
|
$5$ only |
A team scored the following number of goals in each of the six hockey games it played:
Find out the mode of the team's goal distribution.
Let's start by sorting our data set:
The mode is the value that occurs the most often in the data set. We have that:
appears time
appears times
appears times
appears time
The values and both appear more frequently than the others (both times in total).
Therefore, the data set has two modes: and
Noah is a professional baseball pitcher. In his last $7$ games, he achieved the following number of strikeouts: \[ 7, \; 6, \; 8, \; 7, \; 8, \; 7, \; 9 \]
Find the mode of Noah's strikeout distribution.
|
a
|
$6$ |
|
b
|
$3$ |
|
c
|
$9$ |
|
d
|
$7$ |
|
e
|
$8$ |
Mary recorded the monthly growth of her puppy for a period of $8$ months. She obtained the following values:
\[ 3 \, \text{cm}, \quad 4 \, \text{cm}, \quad4 \, \text{cm}, \quad3 \, \text{cm}, \quad2 \, \text{cm},\quad 5 \, \text{cm}, \quad 6 \, \text{cm}, \quad 5 \, \text{cm} \] Find the mode of this data set.
|
a
|
$4\,\text{cm}$ |
|
b
|
$2\,\text{cm}$ and $6\,\text{cm}$ |
|
c
|
$6\,\text{cm}$ |
|
d
|
$3\,\text{cm}$ and $5\,\text{cm}$ |
|
e
|
$3\,\text{cm}, \, 4\,\text{cm},$ and $5\,\text{cm}$ |