Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
Let's tackle the question step by step.
### (a) Construct a frequency distribution table
First, we need to create bins/classes for the marks and count how many marks fall into each class. The classes are as follows:
- 30 - 39
- 40 - 49
- 50 - 59
- 60 - 69
- 70 - 79
- 80 - 89
Then, we count the number of students whose marks fall into each class.
Frequency distribution table:
| Class Interval | Frequency |
|----------------|-----------|
| 30 - 39 | 2 |
| 40 - 49 | 8 |
| 50 - 59 | 11 |
| 60 - 69 | 11 |
| 70 - 79 | 5 |
| 80 - 89 | 3 |
### (b) Draw a histogram for the above data
In a histogram, the x-axis represents the classes (30-39, 40-49, etc.), and the y-axis represents the frequency of marks in those classes.
The histogram bars will look something like this:
```
Frequency
^
11| ________
10| | |
9| | |
8| ________ | |
7| | | | |
6| | | | |
5| | | |______|
4| | | | |
3| | |______ | | _____
2| | | || |_____
1| |______| || | | |
|________________________________________________ Class Intervals
30-39 40-49 50-59 60-69 70-79 80-89
```
### (c) Construct a "less than" cumulative frequency distribution
To construct a "less than" cumulative frequency distribution, we add the frequencies cumulatively from the lowest class to the highest class.
"Less than" cumulative frequency distribution table:
| Class Interval | Cumulative Frequency |
|--------------------|----------------------|
| Less than 40 | 2 |
| Less than 50 | 10 |
| Less than 60 | 21 |
| Less than 70 | 32 |
| Less than 80 | 37 |
| Less than 90 | 40 |
### (d) Draw a "less than" cumulative frequency polygon
A cumulative frequency polygon can be drawn by plotting the cumulative frequencies against the class boundaries. Then, we connect the points with straight lines.
The cumulative frequency polygon will look something like this:
```
Frequency
^
40|
35| _______
30| ______|
25| _________|
20| ________|
15| ___________|
10| ____|
5|______|
0|___________________________________________________ Class Intervals
< 40 < 50 < 60 < 70 < 80 < 90
```
Each point on the polygon represents the cumulative frequency at the upper boundary of each class. For example, at "Less than 50", the cumulative frequency is 10, and so on.
### (a) Construct a frequency distribution table
First, we need to create bins/classes for the marks and count how many marks fall into each class. The classes are as follows:
- 30 - 39
- 40 - 49
- 50 - 59
- 60 - 69
- 70 - 79
- 80 - 89
Then, we count the number of students whose marks fall into each class.
Frequency distribution table:
| Class Interval | Frequency |
|----------------|-----------|
| 30 - 39 | 2 |
| 40 - 49 | 8 |
| 50 - 59 | 11 |
| 60 - 69 | 11 |
| 70 - 79 | 5 |
| 80 - 89 | 3 |
### (b) Draw a histogram for the above data
In a histogram, the x-axis represents the classes (30-39, 40-49, etc.), and the y-axis represents the frequency of marks in those classes.
The histogram bars will look something like this:
```
Frequency
^
11| ________
10| | |
9| | |
8| ________ | |
7| | | | |
6| | | | |
5| | | |______|
4| | | | |
3| | |______ | | _____
2| | | || |_____
1| |______| || | | |
|________________________________________________ Class Intervals
30-39 40-49 50-59 60-69 70-79 80-89
```
### (c) Construct a "less than" cumulative frequency distribution
To construct a "less than" cumulative frequency distribution, we add the frequencies cumulatively from the lowest class to the highest class.
"Less than" cumulative frequency distribution table:
| Class Interval | Cumulative Frequency |
|--------------------|----------------------|
| Less than 40 | 2 |
| Less than 50 | 10 |
| Less than 60 | 21 |
| Less than 70 | 32 |
| Less than 80 | 37 |
| Less than 90 | 40 |
### (d) Draw a "less than" cumulative frequency polygon
A cumulative frequency polygon can be drawn by plotting the cumulative frequencies against the class boundaries. Then, we connect the points with straight lines.
The cumulative frequency polygon will look something like this:
```
Frequency
^
40|
35| _______
30| ______|
25| _________|
20| ________|
15| ___________|
10| ____|
5|______|
0|___________________________________________________ Class Intervals
< 40 < 50 < 60 < 70 < 80 < 90
```
Each point on the polygon represents the cumulative frequency at the upper boundary of each class. For example, at "Less than 50", the cumulative frequency is 10, and so on.
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
