Question

During a medical check-up of $35$ students of a class, their weights were recorded as follows:
$\begin{array}{cc}\text{Weight (in kg)}& \text{Number of students}\\ \text{Less than}38& 0\\ \text{Less than}40& 3\\ \text{Less than}42& 5\\ \text{Less than}44& 9\\ \text{Less than}46& 14\\ \text{Less than}48& 28\\ \text{Less than}50& 32\\ \text{Less than}52& 35\end{array}$
Draw a less than type ogive for the given data.
Hence, obtain the median weight from the graph and verify the result by using the formula.

Answer 1

From the graph, median weight $=46.5\text{kg}$

$\begin{array}{ccc}\text{Class Interval}& \text{Frequency(}{f}_i\text{)}& \text{Cumulative frequency(}cf\text{)}\\ 36-38& 0& 0\\ 38-40& 3& 3\\ 40-42& 2& 5\\ 42-44& 4& 9\\ 44-46& 5& 14\\ 46-48& 14& 28\\ 48-50& 4& 32\\ 50-52& 3& 35\end{array}$

Using formula:
$\bullet$ Here, $n=35$ and $\frac{n}{2}=17.5$. Therefore, median class is $46-48$.

$\bullet$ Here, $l=46,f=14,cf=14$ and $h=2$

$Median=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$

$=46+\left(\frac{17.5-14}{14}\right)\times 2$

$=46+\left(\frac{7}{14}\right)=46+0.5=46.5$

$\bullet$ Therefore, the median weight of the students is $46.5\text{kg}$. The results obtained from the graph and by using the formula are the same. Hence, verified.