Question

The following table shows the weights of 12 students:

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

Find the mean, median and mode for the above data.

Answer 1

Weight (xi)	Number of Students (fi)	Cumulative Frequency	(xi)(fi)
47	4	4	188
50	3	7	150
53	2	9	106
56	2	11	112
60	4	15	240
	n = 15		$\sum _{}^{}{f}_i{x}_i=$796

$$\begin{gathered} \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{observations}\mathrm{is}15,\mathrm{which}\mathrm{an}\mathrm{odd}\mathrm{number}. \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ \mathrm{Median}=\left[{\left(\frac{\mathrm{n}+1}{2}\right)}^{\mathrm{th}}\mathrm{term}\right] \\ =\left[{\left(\frac{15+1}{2}\right)}^{\mathrm{th}}\mathrm{term}\right] \\ =\left[8^{\mathrm{th}}\mathrm{term}\right] \\ =53 \end{gathered}$$

Also,
$$\begin{gathered} \mathrm{Mean}=\frac{{\displaystyle \sum _{}^{}}{f}_i{x}_i}{{\displaystyle \sum _{}^{}}{f}_i} \\ =\frac{796}{15}=53.06 \end{gathered}$$

By the empirical formula, we have:
Mode = 3 Median $-$ 2 Mean
Or,
Mode = 3(53) $-$ 2(53.06) = 52.88