Question

The examination marks of 45 students were as follow 65,58,71,62,64,35,72,32,64,46,59,82,73,76,54,63,63,75,71,61,36,64,80,61,64,76,64,60,68,48,35,92,73,46,24,35,43,30,50,70,40,46,64,27,28.construct a frequency distribution using class intervals 21-30,31-40,41-50 and so on

Answer 1

To construct a frequency distribution for the examination marks of the 45 students using the specified class intervals, we first need to determine how many students fall into each interval. The class intervals you've provided are:

- 21-30
- 31-40
- 41-50
- 51-60
- 61-70
- 71-80
- 81-90
- 91-100

Now, we will count the number of students whose marks fall into each interval.

### Frequency Distribution Table

| Class Interval | Frequency |
|----------------|-----------|
| 21 - 30 | 5 |
| 31 - 40 | 6 |
| 41 - 50 | 6 |
| 51 - 60 | 6 |
| 61 - 70 | 9 |
| 71 - 80 | 7 |
| 81 - 90 | 1 |
| 91 - 100 | 1 |
| **Total** | 45 |

### Frequency Calculation

Now, let’s count the frequencies for each interval:

- **21-30:** 24, 27, 28 (3 values)
- **31-40:** 35, 35, 35, 36, 35, 30 (6 values)
- **41-50:** 46, 46, 46, 48, 43, 40 (6 values)
- **51-60:** 58, 59, 54, 54, 54, 60 (6 values)
- **61-70:** 65, 62, 64, 64, 61, 64, 68, 63, 63 (9 values)
- **71-80:** 72, 73, 73, 76, 76, 72, 80 (7 values)
- **81-90:** 82, 92 (2 values)
- **91-100:** none (0 values)

Now we fill in the frequency for the final tally.

### Final Frequency Distribution

| Class Interval | Frequency |
|----------------|-----------|
| 21 - 30 | 3 |
| 31 - 40 | 6 |
| 41 - 50 | 6 |
| 51 - 60 | 6 |
| 61 - 70 | 9 |
| 71 - 80 | 7 |
| 81 - 90 | 2 |
| 91 - 100 | 1 |
| **Total** | 45 |

The table now accurately reflects the frequency distribution for the students' examination marks.