Question

Calculate the mean, the median, and the mode of the following numbers:

$3,2,6,3,3,1,1,2$

Answer 1

Step 1: Find the mean:

Take the given set of numbers

$3,2,6,3,3,1,1,2$

Arrange given data in ascending order

$1,1,2,2,3,3,3,6$

The sum of data is divided by the number of data.

$Mean = \frac{\sum X_i}{n}$

$Mean = \frac{1+1+2+2+3+3+3+6}{8}$

$Mean = \frac{21}{8}$

$Mean = 2.625$

Step 2: Find the median of the numbers:

The middle number in a list of numbers sorted in ascending or descending order is called the median.

The number of data is $n=8$

$median = \left(\frac{{\left(\frac{n}{2}\right)}^{th}+{\left(\frac{n}{2}+1\right)}^{th}}{2}\right)$

$median = \left(\frac{{\left(\frac{8}{2}\right)}^{th}+{\left(\frac{8}{2}+1\right)}^{th}}{2}\right)$

$median = \frac{1}{2}(4^{th} term + {(4+1)}^{th} term)$

$median = \frac{1}{2}(4^{th} term + 5^{th} term)$

$median = \frac{1}{2}(2+3)$

$median = \frac{1}{2}\times 5$

$median =2.5$

Step 3: Find the mode of the numbers:

$3,2,6,3,3,1,1,2$

Mode is the value that occurs most often in the given number of sets.

In the given set, $3$ occurs the maximum number of times.

So, the mode is $3$.

Hence, the mean, the median, and the mode of $3,2,6,3,3,1,1,2$ is $2.625$, $2.5$ and $3$ respectively.