Question

Given below are the marks obtained by $50$students of class IX in a Hindi test. With this data, prepare a frequency distribution table.
$
  42,21,51,37,42,37,38,,42,49,52,38,53,57,47,29,,59,61,33,17,71,39,44,42,39,14,7,27,19, \\
  54,51,39,43,42,16,37,67,62,39,51,53,41,53,59,37,27,33,34,42,22,31 \\
 $

Answer 1

Hint: We are asked to frame a frequency distribution table. A frequency distribution table is nothing but a table containing values and their frequency. Here, frequency refers to how often that required value occurs.
For example, in data, $5,3,5,4,6,7,5$ the frequency of $5$ is $3$ because $5$ occurs three times.

Complete step by step answer:
Here, we are given data containing marks obtained by $50$ students of class IX in a Hindi test.
The marks are,$
  42,21,51,37,42,37,38,42,49,52,38,53,57,47,29,59,61,33,17,71,39,44,42,39,14,7,27,19, \\
  54,51,39,43,42,16,37,67,62,39,51,53,41,53,59,37,27,33,34,42,22,31 \\
 $
We need to group this data and also we are asked to prepare a frequency distribution table.
Before preparing a frequency distribution table, we shall group this data.
First, we shall arrange this data in ascending order so that it will be easy for us to group them.
$
  7,14,16,17,19,21,22,27,27,29,31,33,33,34,37,37,37,37,38,38,39,39, \\
  39,39,41,42,42,42,42,42,42,43,44,47,49,51,51,51,52,53,53,53,54, \\
  57,59,59,61,62,67,71 \\
 $
Now, we shall calculate the number of students who obtained marks between the intervals $5 - 9$, $10 - 14$ ,$15 - 19$,$20 - 24$, $25 - 29$,$30 - 34$ ,$35 - 39$ ,$40 - 44$ ,$45 - 49$ ,$50 - 54$,$55 - 59$,$60 - 64$,$65 - 69$,$70 - 74$
Thus, the number of students who got marks between the intervals $5 - 9$$ = 1$
The number of students who got marks between the intervals $10 - 14$$ = 1$
The number of students who got marks between the intervals $15 - 19$$ = 3$
The number of students who got marks between the intervals $20 - 24$$ = 2$
The number of students who got marks between the intervals $25 - 29$$ = 3$
The number of students who got marks between the intervals $30 - 34$$ = 4$
The number of students who got marks between the intervals $35 - 39$$ = 10$
The number of students who got marks between the intervals $40 - 44$$ = 9$
The number of students who got marks between the intervals $45 - 49$$ = 2$
The number of students who got marks between the intervals $50 - 54$$ = 8$
The number of students who got marks between the intervals $55 - 59$$ = 3$
The number of students who got marks between the intervals $60 - 64$$ = 2$
The number of students who got marks between the intervals $65 - 69$$ = 1$
The number of students who got marks between the intervals $70 - 74$$ = 1$
Now, let us prepare a frequency distribution table.

Marks obtained	Number of students (frequency)
$5 - 9$	$1$
$10 - 14$	$1$
$15 - 19$	$3$
$20 - 24$	$2$
$25 - 29$	$3$
$30 - 34$	$4$
$35 - 39$	$10$
$40 - 44$	$9$
$45 - 49$	$2$
$50 - 54$	$8$
$55 - 59$	$3$
$60 - 64$	$2$
$65 - 69$	$1$
$70 - 74$	$1$

Note: We shall note the steps that are followed to prepare a frequency distribution table.
First, we need to analyze whether we can group the required data or not. If not, we can find the frequency for each value. Or else, choose the intervals that suit the data.
Then we shall sort the data and find the frequency for each value or each interval.