Question

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

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

Find the median height.

Answer 1

Class interval (exclusive)	Class interval (inclusive)	Class interval (Frequency)	Cumulative frequency
160 - 162	159.5 - 162.5	15	15
163 - 164	162.5 - 165.5	118	133 (F)
166 - 168	165.5 - 168.5	142 (f)	275
169 - 171	171.5 - 174.5	18	420
172 - 174	171.5 - 174.5	18	420
		N = 420

We have, 

N = 420

\(\frac{N}{2}=\frac{420}{2}=210\)

The cumulative frequency just greater than \(\frac{N}{2}\) is 275 then 165.5-168.5 is the median class such that,

I = 165.5, f = 142, F = 133 and h = 168.5-165.5 = 3

Median = I + \(\frac{\frac{N}{2}-F}{f}\times h\)

\(=165.5+\frac{210-133}{142}\times 3\)

\(=165.5+\frac{77}{142}\times 3\)

\(=165.5+1.63\)

\(=167.13\)