The following table shows the weights of 15 students :

Weight (in kg)	Number of students
47	4
50	3
53	2
56	2
60	4

Calculate :

(i) mean

(ii) median

(iii) mode

The variates are already in ascending order. We construct the cumulative frequency table as under:

Total number of observations = 15, which is odd.

(i) By formula,

$\Rightarrow \text{Mean} = \dfrac{\sum\text{fx}}{\sum\text{f}} \\[1em] \Rightarrow \text{Mean} = \dfrac{796}{15} \\[1em] \Rightarrow \text{Mean} = 53.06$

Hence, mean = 53.06.

(ii) By formula,

Median = $\dfrac{\text{n} + 1}{2} \text{ th observation}$

$= \dfrac{15 + 1}{2} \text{ th observation} \\[1em] = \dfrac{16}{2} \text{ th observation} \\[1em] = 8 \text{ th observation} \\[1em]$

Cumulative frequencies 8th and 9th corresponds to 53 kg.

Hence, median = 53 kg.

(iii) The highest frequency is 4.

4 corresponds to two weight = 47 kg and 60 kg.

Hence, mode = 47 kg and 60 kg.