Solve this:
8.The following table gives the frequency distribution of marks obtained by 199 students in an examination:
Marks | No. of students |
0-20 | 21 |
21-30 | 19 |
31-40 | 60 |
41-50 | 42 |
51-60 | 24 |
61-70 | 18 |
71-80 | 15 |
Dear student,
The given frequency distribution is an inclusive series. It can be converted into an exclusive series as follows:
In a grouped frequency table we assume that the frequencies are evenly distributed. Accordingly, for the class interval (30.5 - 40.5) we can assume that half of the frequency (i.e.30) lies in (30.5 - 35.5).
So, the total number of students who have marks less than 35.5 are 21 + 19 + 30 = 70. This is equal to 35.2% of the total number of students (i.e. 70/199)
The given frequency distribution is an inclusive series. It can be converted into an exclusive series as follows:
Class Interval | Frequency |
-0.5 - 20.5 | 21 |
20.5 - 30.5 | 19 |
30.5 - 40.5 | 60 |
40.5 - 50.5 | 42 |
50.5 - 60.5 | 24 |
60.5 - 70.5 | 18 |
70.5 - 80.5 | 15 |
In a grouped frequency table we assume that the frequencies are evenly distributed. Accordingly, for the class interval (30.5 - 40.5) we can assume that half of the frequency (i.e.30) lies in (30.5 - 35.5).
So, the total number of students who have marks less than 35.5 are 21 + 19 + 30 = 70. This is equal to 35.2% of the total number of students (i.e. 70/199)