Question

Heights of 50 students of class X of a school are recorded and following data is obtained:

Height (in cm)	130 – 135	135 – 140	140 – 145	145 – 150	150 – 155	155 – 160
Number of students	4	11	12	7	10	6

Find the median height of the students.

Answer 1

Let us first construct the table of cumulative frequency as shown below:

Height (in cm)	Number of students (fi)	Cucumulative Frequency (c.f.)
130 – 135	4	4
135 – 140	11	15
140 – 145	12	27
145 – 150	7	34
150 – 155	10	44
155 – 160	6	50
Total	`sum"f"_"i"` = 50

Here, `"N"/2 = 50/2` = 25, which lies in cumulative frequency of 27

∴ The median class is 140 – 145.

So, l = 140, c.f. = 15, f = 12 and h = 5

Now, as median (M_e) = `"l" + ("N"/2 - "c.f.")/"f" xx "h"`

∴ Required median = `140 + (25 - 15)/12 xx 5`

= `140 + 10/12 xx 5`

= 140 + 4.17

= 144.17