Question

The mean, median, and mode of a data set are $33.667,34$, and $35$, respectively. Find out which data set follows these.

• A. $30,32,33,35,35,36$
• B. $33,34,29,35,36,35$
• C. $32,33,31,35,36,35$
• D. $35,35,34,30,30,31$

Answer 1

The correct option is C $32,33,31,35,36,35$

Option A:
Data set: $33,34,29,35,36,35$
$\text{Mean}=\frac{\text{Sum of the data}}{\text{number of data values}}$

$\text{Mean}=\frac{33+34+29+35+36+35}{6}$
$\text{Mean}=\frac{202}{6}=33.667$
The data set in the ascending order is $29,33,34,35,35,36$.
For a data set with an even number of values, the median is the mean of the two middle values.
As the data set has $6$ values, the median will be the mean of the 3rd and 4th values.

$\text{Median}=\frac{34+35}{2}=34.5$
The mode of a data set is the value that occurs most often; hence, $35$ is the mode.
Option A is incorrect.

Option B:
Data set: $35,35,34,30,30,31$
$\text{Mean}=\frac{\text{Sum of the data}}{\text{number of data values}}$

$\text{Mean}=\frac{35+35+34+30+30+31}{6}$
$\text{Mean}=\frac{195}{6}=32.5$
The data set in the ascending order is $30,30,31,34,35,35.$
For a data set with an even number of values, the median is the mean of the two middle values.
As the data set has $6$ values, the median will be the mean of the 3rd and 4th values.

$\text{Median}=\frac{31+34}{2}=32.5$
The mode of a data set is the value that occurs most often; hence, $35$ and $30$ is the mode.
Option B is incorrect.

Option C:
Data set: $32,33,31,35,36,35$
$\text{Mean}=\frac{\text{Sum of the data}}{\text{number of data values}}$

$\text{Mean}=\frac{32+33+31+35+36+35}{6}$
$\text{Mean}=\frac{202}{6}=33.667$
The data set in the ascending order is $31,32,33,35,35,36.$
For a data set with an even number of values, the median is the mean of the two middle values.
As the data set has $6$ values, the median will be the mean of the 3rd and 4th values.

$\text{Median}=\frac{33+35}{2}=34$
The mode of a data set is the value that occurs most often; hence, $35$ is the mode.
Option C is correct.

Option D:
Data set: $30,32,33,35,35,36$
$\text{Mean}=\frac{\text{Sum of the data}}{\text{number of data values}}$

$\text{Mean}=\frac{30+32+33+35+35+36}{6}$
$\text{Mean}=\frac{201}{6}=33.5$
The data set in the ascending order is $30,32,33,35,35,36.$
For a data set with an even number of values, the median is the mean of the two middle values.
As the data set has $6$ values, the median will be the mean of the 3rd and 4th values.

$\text{Median}=\frac{33+35}{2}=34$
The mode of a data set is the value that occurs most often; hence, $35$ is the mode.
Option D is incorrect.