Question

The table below gives the volume of water (in litres) Suzanne drank in the last 40 days. Find the median of this data.
$$\begin{array}{cc}Volume& Number\\ ofwater\left(l\right)& ofdays\\ 1-2& 6\\ 2-3& 8\\ 3-4& 12\\ 4-5& 6\\ 5-6& 8\end{array}$$

• A. 2
• B. 3.5
• C. 4
• D. 5.5

Answer 1

The correct option is B 3.5

$\begin{array}{cc}Volume& Cumulative\\ ofwater\left(l\right)& frequency\\ 1-2& 6\\ 2-3& 14\\ 3-4& 26\\ 4-5& 32\\ 5-6& 40\end{array}$

Here, N = 40.
$\Rightarrow \frac{N}{2}=20$
$\therefore$ Median class is 3-4.

The formula for median of a grouped data is given by,

$M=L+\left[\frac{\frac{n}{2}-cf}{f}\right]\times h$
where,
M = median of the grouped data
L = Lower limit of median class
n = Sum of frequencies
cf = Cumulative frequency of the class preceding the median class
f = frequency of the median class
and, h = class size

Substituting the given values, we get:

$Median=3+\frac{\frac{40}{2}-14}{12}\times 1=3+\frac{6}{12}=3+\frac{1}{2}=3.5$