Question

The marks of $24$ candidates in the subject mathematics are given below:
\[45,48,15,23,30,35,40,11,29,0,3,12,48,50,18,30,15,30,11,42,23,2,3,44\]
The maximum marks are $50$. Make a frequency distribution taking class intervals $0 - 10,10 - 20,........$

Answer 1

Hint: Here we will first arrange the numbers in ascending order and then fill them in the specific class interval which is given to us. Finally we get the required answer.

Complete step-by-step solution:
It is given that the question stated as the marks of $24$ students given to us as:
\[45,48,15,23,30,35,40,11,29,0,3,12,48,50,18,30,15,30,11,42,23,2,3,44\]
Now we have to construct the data as in ascending order.
\[0,2,3,3,11,11,12,15,15,15,18,23,23,29,30,30,30,35,40,42,44,45,48,48,50\]
From the question we know that the maximum marks of the test are $50$.
Therefore, the class intervals in which the marks will be put in will be $0 - 10,10 - 20,20 - 30,30 - 40,40 - 50.$ each having a gap of total $10$ marks.
Now in the interval $0 - 10$ the numbers which will be put are: $0,3,2,3$
So the total numbers of candidates who have marks in the class interval $0 - 10$ are: $4$
Now in the interval $10 - 20$ the numbers which will be put are: $15,11,12,18,15,11$
So, the total numbers of candidates who have marks in the class interval $10 - 20$ are $6$.
Again, in the interval $20 - 30$ the numbers which will be put are: $23,29,23$
So, the total numbers of candidates who have marks in the class interval $20 - 30$ are $3$.
Also, we take the interval $30 - 40$ the numbers which will be put are: $30,35,30,30$
So, the total numbers of candidates who have marks in the class interval $30 - 40$ are $4$.
Now in the interval $40 - 50$ the numbers which will be put are: $45,48,40,48,50,42,44$
So, the total numbers of candidates who have marks in the class interval $40 - 50$ are $7$.
Therefore, the frequency table could be made as:

Class interval	Frequency
$0 - 10$	$4$
$10 - 20$	$6$
$20 - 30$	$3$
$30 - 40$	$4$
$40 - 50$	$7$
Total	$24$

Note: The application of a frequency table is to find the mean, median and mode of grouped data. It is also used to create a cumulative frequency curve also called an ogive.
The frequency table made in the above problem has the class intervals which are continuous.