Question

In a hospital, weights of new born babies were recorded, for one month. Data is as shown:

Weight of new born baby (in kg)	1.4 - 1.8	1.8 - 2.2	2.2 - 2.6	2.6 - 3.0
No of babies	3	15	6	1

Then the median weight is?

Options

• 2kg

• 2.03kg

• 2.05kg

• 2.08kg

Answer 1

2.05kg

Explanation:-

Construct a table as follows:

Class interval	Frequency (fi)	Midpoint (xi)	Cumulative Frequency (cf)
1.4 - 1.8	3	1.6	3
1.8 - 2.2	15	2	18
2.2 - 2.6	6	2.4	24
2.6 - 3.0	1	2.8	25

Since ${\displaystyle \frac{N}{2}=\frac{25}{2}=12.5}$

12.5 is near to cumulative frequency value 18

So median class interval is 1.8 - 2.2

∴ Median = ${\displaystyle l+\frac{\frac{\frac{N}{2}-cf}{f}}{h}}$

Here

l = 1.8

${\displaystyle \frac{N}{2}=\frac{25}{2}}$

${\displaystyle \Rightarrow \frac{N}{2}=12.5}$

cf = 3

f = 15

h = 0.4

Therefore,

${\displaystyle \text{Median}=l+\left[\frac{\frac{N}{2}-cf}{f}\right]h}$

${\displaystyle =1.8+\left[\frac{12.5-3}{15}\right]0.4}$

= 1.8 + 0.25

= 2.05

Hence median weight is 2.05 kg.