Question

Write the marks wise frequencies in the following frequency distribution table.

Marks	Up to 5	Up to 6	Up to 7	Up to 8	Up to 9	Up to 10
No. of students	5	11	19	31	40	45

Answer 1

Hint: The first column will be the marks. We know that up to 5 marks mean 0-5, up to 6 means 0-6, up to 7 means 0-7, and so on. We know that the mark wise frequency denotes the upper range of marks and their corresponding frequencies. Hence, we will denote up to 5 as mark 5, up to 6 as mark 6, and so on. In the next column, we will denote the number of students scoring these marks, that is, the given number of students. The last column is the frequency. Initially, it will be the same as the number of students for mark 5 only. For further marks, we have found the frequency by subtracting the number of students who scored the previous mark from the current number of students.

Complete step-by-step solution:
We have to write the mark wise frequencies in the given frequency distribution table.
The first column will be the marks. We know that up to 5 marks mean 0-5, up to 6 means 0-6, up to 7 means 0-7, and so on. We know that the mark wise frequency denotes the upper range of marks and their corresponding frequencies. Hence, we will denote up to 5 as mark 5, up to 6 as mark 6, up to 7 as mark 7, up to 8 as mark 8, up to 9 as mark 9, and up to 10 as mark 10.
In the next column, we will denote the number of students scoring these marks, that is, the given number of students.
The last column is the frequency. Initially, it will be the same as the number of students for mark 5 only. For further marks, we have found the frequency by subtracting the number of students who scored the previous mark from the current number of students. We find the frequency in this way because it is given that, say, 5 students scored marks up to 5 and 11 students scored marks up to 6. Here, these 11 students also include the 5 students from up to 5 categories. So we will perform subtraction to find the number of students that got marks within 5-6.
Now, let’s create the mark wise frequency distribution table.

Marks	No. of students	Frequencies(f)
5	5	5
6	11	$11-5=6$
7	19	$19-11=8$
8	31	$31-19=12$
9	40	$40-31=9$
10	45	$45-40=5$

Note: You may make mistakes by subtracting the frequency of the previous mark from the current number of students. For example, you may do $19-4=15$ for mark 7. This leads to wrong results. There can be a chance of error when changing the marks, say up to 6, to its mark wise frequency by writing 5-6 instead of 6.