Question

Calculate the mean and median of the following grade point averages:

3.2, 2.5, 2.1, 3.7, 2.8, 2.0

Short answer

The mean is 2.71.

The median is 2.65.

Step-by-step solution

Calculating the mean

The mean $\overline{\text{X}}$is the average of all the observations.

$$\begin{gathered} \overline{\text{X}}=\frac{\sum _{}\text{X}}{\text{N}} \\ =\frac{\left(\text{3.2+2.5+2.1+3.7+2.8+2.0}\right)}{\text{6}} \\ =\frac{\text{16.3}}{\text{6}} \\ =2.72 \end{gathered}$$

Therefore, the mean grade point average is 2.72.

Computing the median

The median is the centermost observation. We will arrange the grade points in ascending order.

2.0, 2.1, 2.5, 2.8, 3.2, 3.7

As there is an even number of observations, the median will be as follows:

$$\begin{gathered} \mathbf{\text{Median:}}\mathbf{=}\frac{2.5+2.8}{2} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}=\frac{5.3}{2} \\ =2.65 \end{gathered}$$

Thus, the median grade point average score is 2.65.