Question

What is the median class for the following data set given below:

Time (in min)	10-20	20-30	30-40	40-50
Running Race (in km)	10	20	3	4

(A) 10-20
(B) 20-30
(C) 30-40
(D) 40-50

Answer 1

Hint: Median is described as the “central” data set. This means if we organize a particular data set in its increasing order, then the median is said to be the data that lies in the center of this arrangement. This means median is a quality that belongs to any group member. Based on the value distribution in our data set, the mean may not be particularly close to the quality of any group member.

Complete step by step solution:
The median of any data set is the middle most value of the data-set. And the class in which this middle most or ‘median’ lies is known as the median class.
Now, the data set given to us is:

Time (in min)	10-20	20-30	30-40	40-50
Running Race (in km)	10	20	3	4

The formula to calculate the median class of any data set is given by:
Median class is equal to:
$=\dfrac{\left( \text{Total number of frequencies +1} \right)}{2}$
Let the total number of frequencies of our data set be ‘f’. Then, this can be calculated by adding all the individual frequencies of all the individual data-sets. This is done as follows:
$\begin{align}
  & \Rightarrow f=10+20+3+4 \\
 & \therefore f=37 \\
\end{align}$

Now, putting this value of total number of frequencies in the equation of median class, we get the median class as:
$\begin{align}
  & =\dfrac{37+1}{2} \\
 & =19 \\
\end{align}$

Thus, our median class comes out to be 19. Now, we will check from our data set, in which interval does this value lie.
It lies in the interval of 10-20.
Hence, the median class for the given data set comes out to be 10-20.

So, the correct answer is “Option A”.

Note: There is one very important relation between the mean, median and mode of any given data set. This was first given by Karl Pearson. The formula states that, the mean, median and mode of any data set is related as: $\text{Mode = 3Median - 2Mean}$. It is one of the most important formula of statistics.