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

The median height is 167 c.m

Answer 2

Answer:

168.5

Step-by-step explanation:

Class interval     Class interval   Class interval    Cumulative

(exclusive)            (inclusive)       frequency        frequency

160 – 162 159.5 – 162.5         15                     15

163 – 165 162.5 – 165.5          118                    133 (F)

166 – 168 165.5 – 168.5          142 (f)              275

169 – 171           168.5 – 171.5          127                       402

172 – 174           171.5 – 174.5            18                        420

Sum of frequencies = 15+118+142+127+18 = 420

N = 420

$\frac{n}{2}=\frac{420}{2}=210$

The cumulative frequency just greater than N/2 is 275

So, 165.5 – 168.5 is the median class

L = lower limit = 165.5

f = 142

F = 133

h = class height = 168.5 – 165.5 = 3

Formula :$median = L+\frac{\frac{n}{2}-F}{f} \times h$

So, $Median =165.5+\frac{275-133}{142} \times 3$

$Median =168.5$

Hence the median is 168.5