Question

The following are score earned by 15 college students on a 20-point math quiz. (a) calculate the mean, median, and mode scores. (b) identify which measure in part (a) is most representative of the data. 0, 2, 3, 12, 12, 13, 14, 14, 15, 15, 18, 18, 18, 19, 20 (a) the mean score is ( ).

Answer 1

(a) 12.87; 14; 18; (b) median

Explanation:

(a) Statistics

(i) Mean

The mean is the sum of all the data points divided by the number of points.

`\begin{array}{rcl}\text{Mean} & = & (0 + 2 + 3 + 12 + 12 + 13 + 14 + 14 + 15 + 15 + 18 + 18 + 18 + 19 + 20)/(15)\\\\& = & (193)/(15)\\\\& = & \mathbf{12.87}\\\end{array}`

(ii) Median

The median is the middle value in your list of observations.

0, 2, 3, 12, 12, 13, 14, 14, 15, 15, 18, 18, 18, 19, 20

Median = 14

(iii) Mode

The mode is the value that appears most often in your list of observations.

0, 2, 3, 12, 12, 13, 14, 14, 15, 15, 18, 18, 18, 19, 20

Mode = 18

(b) Most representative measure

The mean is dragged down by three low values. The median is the measure that is most representative of the data.

The histogram below shows the distribution of your data.