Question
Question: The following are the marks (out of 100) of 60 students in mathematics. 16, 13, 5, 80, 86, 7, 51, 48...
The following are the marks (out of 100) of 60 students in mathematics. 16, 13, 5, 80, 86, 7, 51, 48, 24, 56, 70, 19, 61, 17, 16, 36, 34, 42, 34, 35, 72, 55, 75, 31, 52, 28, 72, 97, 74, 45, 62, 68, 86, 35, 85, 36, 81, 75, 55, 26, 95, 31, 7, 78, 92, 62, 52, 56, 15, 63, 25, 36, 54, 44, 47, 27, 72, 17, 4, 30. Construct a grouped frequency distribution table with width 10 of each class starting from 0-9.
Solution
Hint: To solve the question given above, we will first arrange the marks in ascending order. Then, we will calculate the total number of marks which are present in 0-9. Then we will calculate the total number of marks which are present in 10-99. We will do the same for the succeeding class and we will determine the frequency in each case. We will form the table in which one column will be of class interval and another will be of frequency.
Complete step-by-step answer:
The first thing we will do before making grouped frequency distribution table is to arrange the marks of the students in ascending order: 4, 5, 7, 7, 13, 15, 16, 17, 17, 19, 24, 25, 26, 27, 28, 30, 31, 34, 34, 34, 35, 35, 36, 36, 36, 42, 44, 45, 47, 48, 51, 52, 52, 54, 55, 55, 56, 56, 61, 62, 62, 63, 68, 70, 72, 72, 72, 74, 75, 75, 78, 80, 81, 85, 86, 92, 95, 97.
Now, it is given in the question that the width of each class is 10 and it starts from 0-9. The next class will be 10-19. The next class will be 20-29 and so on. Now, we will count how many marks are present in each class. The frequency of 0-9 will be 4. The frequency of 10-19 is 7. The frequency of 20-29 is 5 and so on. Now, we will make the grouped frequency distribution table:
| Marks of 60 students (class interval) | Frequency |
|---|---|
| 0 – 9 | 4 |
| 10 – 19 | 7 |
| 20 – 29 | 5 |
| 30 – 39 | 10 |
| 40 – 49 | 5 |
| 50 – 59 | 8 |
| 60 – 69 | 5 |
| 70 – 79 | 8 |
| 80 – 89 | 5 |
| 90 – 99 | 3 |
Note: It is not necessary to arrange the marks of the given 60 students in ascending order to make a grouped frequency distribution table. We have arranged the data in increasing order to make sure that there is no error. Also if we want to check whether the frequencies of class written by us is correct or not, we will add all the frequencies. If the sum is equal to 60, then we have written correct frequencies.