Question

The heights (in cm) of 50 students of a class are given below.

Height (in cm)	156	154	155	151	157	152	153
No. of students	8	4	10	6	7	3	12

Find the median height.

Answer 1

The following table represents heights of students in ascending order:

Height (cm)	No. of Students	Cumulative Frequency
151	6	6
152	3	9
153	12	21
154	4	25
155	10	35
156	8	43
157	7	50
	n = 50

$$\begin{gathered} \mathrm{Here},\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{observations}\mathrm{is}50,\mathrm{which}\mathrm{is}\mathrm{an}\mathrm{even}\mathrm{number}. \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ \mathrm{Median}=\frac{1}{2}\left[{\left(\frac{\mathrm{n}}{2}\right)}^{\mathrm{th}}\mathrm{term}+{\left(\frac{\mathrm{n}}{2}+1\right)}^{\mathrm{th}}\mathrm{term}\right] \\ =\frac{1}{2}\left[{\left(\frac{50}{2}\right)}^{\mathrm{th}}\mathrm{term}+{\left(\frac{50}{2}+1\right)}^{\mathrm{th}}\mathrm{term}\right] \\ =\frac{1}{2}\left[{25}^{\mathrm{th}}\mathrm{term}+{\left(26\right)}^{\mathrm{th}}\mathrm{term}\right] \\ =\frac{1}{2}[155+155] \\ =155\mathrm{cm} \end{gathered}$$