Question

Find the mean, median, and mode of the following marks obtained by $16$ students in a class test marked out of mark:

$0,0,2,2,3,3,4,5,5,5,5,6,6,7,8$$16$

Answer 1

Step 1: Calculation of the Mean value:

Mean,$\overline{x}=\frac{\sum x_i}{n}$

$\overline{x}=\frac{0+0+2+2+3+3+4+5+5+5+5+6+6+7+8}{16}$

$\overline{x}=\frac{64}{16}$

$\overline{x}=4$

So, the mean value is $4$.

Step 2: Calculation of the Median value:

The median of the given data can be found by the formula,

Since, $n$ is even,

the Median$=\frac{1}{2}\left[{\left(\frac{n}{2}\right)}^{\mathbf{th}}\text{term}+{\left(\frac{n}{2}+1\right)}^{\mathbf{th}}\text{term}\right]$

$=\frac{1}{2}\left[{\left(\frac{16}{2}\right)}^{th}\text{term}+{\left(\frac{16}{2}+1\right)}^{th}\text{term}\right]$

$=\frac{1}{2}\left[8^{th}\text{term}+9^{th}\text{term}\right]$

$=\frac{1}{2}\left[\text{5}+\text{5}\right]$

$=\frac{10}{2}=5$

So, the median value is $5$.

Step 3: Finding the mode value:

Mode is the value of the variation of which frequency is maximum.

In the given data, $5$ appears maximum number of times.

So, the mode is $5$.

Hence, the mean, median, and mode of the marks obtained by $16$ students in a class test is $4$, $5$, and $5$ respectively.