Question

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

Height (in cm)	156	154	155	151	157	152	153
Number of students	8	4	10	6	7	3	12

Find the median height.

Answer 1

We will first arrange the given data in ascending order as follows:

Height (in cm)	Number of Students
151	6
152	3
153	12
154	4
155	10
156	8
157	7

Now, we will prepare the cumulative frequency table as follows:

Height (in cm)	Frequency	Cumulative Frequency
151	6	6
152	3	9
153	12	21
154	4	25
155	10	35
156	8	43
157	7	50

Here, n is 50, which is an even number.
Thus, we have:
$\mathrm{Median}=\mathrm{Mean}\mathrm{of}\left(\frac{n}{2}\right)\mathrm{th}\&\left(\frac{n}{2}+1\right)\mathrm{th}\mathrm{observations}$
$$\begin{gathered} \mathrm{Median}\mathrm{height}=\mathrm{Mean}\mathrm{of}\mathrm{the}\mathrm{heights}\mathrm{of}\left(\frac{50}{2}\right)\mathrm{th}\mathrm{and}\left(\frac{50}{2}+1\right)\mathrm{th}\mathrm{students} \\ =\mathrm{Mean}\mathrm{of}\mathrm{the}\mathrm{heights}\mathrm{of}\mathrm{the}25\mathrm{th}\mathrm{and}26\mathrm{th}\mathrm{students} \\ \mathrm{Here},\mathrm{we}\mathrm{see}\mathrm{that}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}25\mathrm{th}\mathrm{student}\mathrm{is}154\mathrm{cm}\&\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}26\mathrm{th}\mathrm{to}35\mathrm{th}\mathrm{students}\mathrm{is}155\mathrm{cm}. \\ \mathrm{Median}\mathrm{height}=\frac{1}{2}\left(154+155\right)\mathrm{cm}=154.5\mathrm{cm} \end{gathered}$$