Question

The marks scored by 20 students in a test are given as: 54, 42, 68, 56, 62, 71, 78, 51, 72, 53, 44, 58, 43, 64, 41, 57, 89, 53, 84, 57. Make a frequency table for the data.

Answer 1

There are 20 data to put in the frequency table. So, we arrange the points in order. We take the lowest and highest number to makes classes. These classes are of equal width. Then with the help of classes, we put all the data in their respective boxes.

Complete step-by-step solution:
The given observations are marks scored by 20 students.
So, the total number of frequencies is 20. We take $n=20$.
The points are 54, 42, 68, 56, 62, 71, 78, 51, 72, 53, 44, 58, 43, 64, 41, 57, 89, 53, 84, 57.
We find the lowest and highest number to makes classes. They are 41 and 89 respectively.
We have to take classes with first-class having lower bound less than or equal to 41 and last class having upper bound equal or greater than 89.
We take in total 5 classes, each with an equal width of 10.
The classes are 41-50, 51-60, 61-70, 71-80, 81-90.
There is no overlapping in the classes. So, all the data can be placed in their respective class.
Classes are termed as ${{x}_{i}}$. The frequency of i-th class is termed as ${{f}_{i}}$, $i=1(1)5$.
Now we place all the 20 data in the table and get

class-interval (${{x}_{i}}$)	frequency (${{f}_{i}}$)
41-50	4
51-60	8
61-70	3
71-80	3
81-90	2
Total (n)	20

Thus, the observations are placed in the frequency table.

Note: The choice of classes can be done in any kind of way. The only thing to remember is that the boundary of the frequencies is covered. We can take the width of the classes smaller but that will increase the number of classes. In that case, the frequencies will be more spread out. We take the help of tally-mark if the counting of the points is difficult.