Question

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

18 10 15 13 17 15 12 15 18 16 11

Short answer

Mean = 14.54

Median = 15

Mode = 15

Step-by-step solution

Calculating the mean

Mean can be computed using the formula:

$$\begin{gathered} \mathbf{Mean} \mathbf{=}\frac{ \mathbf{Summation} \mathbf{of} \mathbf{observations}}{\mathbf{Total} \mathbf{number} \mathbf{of} \mathbf{observations}} \\ \mathbf{Mean} \mathbf{=}\frac{\mathbf{18}\mathbf{+}\mathbf{10}\mathbf{+}\mathbf{15}\mathbf{+}\mathbf{13}\mathbf{+}\mathbf{17}\mathbf{+}\mathbf{15}\mathbf{+}\mathbf{12}\mathbf{+}\mathbf{15}\mathbf{+}\mathbf{18}\mathbf{+}\mathbf{16}\mathbf{+}\mathbf{11}}{\mathbf{11}} \\ \mathbf{Mean} \mathbf{=} \mathbf{14}\mathbf{.}\mathbf{54} \end{gathered}$$

Therefore, the mean is 14.54.

Computing the median

Median is the central value when the total number of observations in a series is an odd number. In the given case, the total terms are 11 (Odd). Therefore, the median will be the middle value in the series when arranged in ascending order.

Arranging the data in ascending order:

10, 11, 12, 13, 15,15,15,16,17,18,18

Hence, the median is 15.

Determining the mode

Mode is the value that has been repeated the highest number of times.

Values	Frequency
18	2
10	1
15	3
13	1
17	1
12	1
16	1
11	1

As can be observed from the table, 15 is repeated 3 times.

Thus, the mode is 15.