Question

The following is the distribution of height of students of a certain class in a certain city:

Height (in cm):	160 - 162	163 - 165	166 - 168	169 - 171	172 - 174
No. of students:	15	118	142	127	18

Find the median height.

Answer 1

First we prepare the following cummulative table to compute the median.

Height (in cm)	Frequency (f1)	Cumulative Frequency (c.f)
160 - 162	15	15
163 - 165	118	133
166 - 168	142	275
169 - 171	127	402
172 - 174	18	420
	N = 420

Now, N = 420

${\displaystyle \therefore \frac{N}{2}=\frac{420}{2}=210}$

Thus, the cumulative frequency just greater than 210 is 275 and the corresponding class is 166 - 168.

Therefore, 166 - 168 is the median class.

l = 166, f = 142, F = 133 and h = 2

We know that,

Median ${\displaystyle =l+\left\{\frac{\frac{N}{2}-F}{f}\right\}\times h}$

${\displaystyle =166+\left\{\frac{210-133}{142}\right\}\times 2}$

${\displaystyle =166+\frac{77\times 2}{142}}$

${\displaystyle =166+\frac{154}{142}}$

= 166 + 1.08

= 167.08

Hence, the median height is approximately 167.1 cm.