The ages of 8 students are: 11, 13, 12, 14, 11, 15, 12, 13.

(a) Find the mean and median of the data

(b) Which value (mean or median) do you think best represents the central tendency of this data? Explain why.

Given ages : 11, 13, 12, 14, 11, 15, 12, 13.

(a) By formula,

$\Rightarrow \text{Mean} = \dfrac{\text{Sum of all observations}}{\text{Number of observations}} \\[1em] = \dfrac{11 + 13 + 12 + 14 + 11 + 15 + 12 + 13}{8} \\[1em] = \dfrac{101}{8} \\[1em] = 12.625.$

To find the median, arrange the ages in ascending order :

11, 11, 12, 12, 13, 13, 14, 15.

There are 8 observations (an even number), so the median is the average of the 4th and 5th observations.

$\Rightarrow \text{Median} = \dfrac{12 + 13}{2} \\[1em] = \dfrac{25}{2} \\[1em] = 12.5.$

Hence, Mean = 12.625 and Median = 12.5

(b) The median best represents the central tendency of this data. The median (12.5) lies exactly in the middle of the data and is not affected by the higher value 15, whereas the mean (12.625) is slightly pulled upward by that larger value.

Hence, the median best represents the central tendency of this data.