Question

In a hospital, weights of new born babies were recorded,
for one month. Data is as shown:
Weight of new born 1.4 - 1.8 - 2.2 - 2.6 -
baby (in kg)
1.8 2.2 2.6 3.0
No of babies
3
15
6
1
Then the median weight is:
A) 2 kg
B) 2.03 kg
C) 2.05 kg
D) 2.08 kg​

Answer 1

Given is data about weights of newborn babies, Find the median weight.

Explanation:

• Given below is the table for the class of weights, the number of babies having their weights in that class, and cumulative frequency corresponding to each class:     $Weight\ (kg)\ \ \ \ \ \ \ \ \ \ \ \ No.\ of\ babies\ \ \ \ \ \ \ \ \ cf\\1.4-1.8\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3\\1.8-2.2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 15 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 18\\2.2-2.6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 24\\2.6-3.0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 25$    
• In order to find the median first we need to find the median class, The first class having 'cf' greater or equal to $\frac{\sum f}{2}=\frac{25}{2}=12.5$
• Hence, the second class $1.8-2.2$ is the median class and the class size is $0.4$.
• Now the median from the median class is given by, $M_d=l+(\frac{\frac{\sum f}{2}-F }{f_m} )C$
• Here, 'l' is the lower boundary, 'F' is the cf of class before the median class, 'fm' is the frequency of median class, 'C' is class size.
• Hence putting above data in the formula we get the median,      $M_d=1.8+(\frac{12.5-3}{15} )0.4 \\\\->M_d= 2.05\bar 3 = 2.05\ kg(approx.)$
• The median of the data is (C)2.05 kg