Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
Let's construct the cumulative frequency distribution and the cumulative relative frequency distribution step-by-step:
### Step 1: Class Intervals and Frequencies
The given class intervals and their frequencies are:
| Class | Frequency |
|--------|-----------|
| 20-29 | 10 |
| 30-39 | 14 |
| 40=49 | 17 |
| 50-59 | 7 |
| 60-69 | 2 |
### Step 2: Cumulative Frequency
To find the cumulative frequency, we sum the frequencies progressively:
- For the interval 20-29: Cumulative frequency is 10.
- For the interval 30-39: Cumulative frequency is [tex]\(10 + 14 = 24\)[/tex].
- For the interval 40=49: Cumulative frequency is [tex]\(24 + 17 = 41\)[/tex].
- For the interval 50-59: Cumulative frequency is [tex]\(41 + 7 = 48\)[/tex].
- For the interval 60-69: Cumulative frequency is [tex]\(48 + 2 = 50\)[/tex].
So, the cumulative frequencies are:
| Class | Cumulative Frequency |
|---------------------- |----------------------|
| Less than or equal to 29 | 10 |
| Less than or equal to 39 | 24 |
| Less than or equal to 49 | 41 |
| Less than or equal to 59 | 48 |
| Less than or equal to 69 | 50 |
### Step 3: Cumulative Relative Frequency
To find the cumulative relative frequency, we divide each cumulative frequency by the total frequency. The total frequency is the sum of all frequencies, which is [tex]\(10 + 14 + 17 + 7 + 2 = 50\)[/tex].
- For the interval 20-29: Cumulative relative frequency is [tex]\(\frac{10}{50} = 0.2\)[/tex].
- For the interval 30-39: Cumulative relative frequency is [tex]\(\frac{24}{50} = 0.48\)[/tex].
- For the interval 40=49: Cumulative relative frequency is [tex]\(\frac{41}{50} = 0.82\)[/tex].
- For the interval 50-59: Cumulative relative frequency is [tex]\(\frac{48}{50} = 0.96\)[/tex].
- For the interval 60-69: Cumulative relative frequency is [tex]\(\frac{50}{50} = 1.0\)[/tex].
So, the cumulative relative frequencies are:
| Class | Cumulative Relative Frequency |
|----------------------- |-------------------------------|
| Less than or equal to 29 | 0.2 |
| Less than or equal to 39 | 0.48 |
| Less than or equal to 49 | 0.82 |
| Less than or equal to 59 | 0.96 |
| Less than or equal to 69 | 1.0 |
Combining both cumulative frequency and cumulative relative frequency distributions:
| Class | Cumulative Frequency | Cumulative Relative Frequency |
|----------------------- |----------------------|-------------------------------|
| Less than or equal to 29 | 10 | 0.2 |
| Less than or equal to 39 | 24 | 0.48 |
| Less than or equal to 49 | 41 | 0.82 |
| Less than or equal to 59 | 48 | 0.96 |
| Less than or equal to 69 | 50 | 1.0 |
These distributions help us understand the accumulation of frequencies and the proportion of the total frequency that falls within or below each class interval.
### Step 1: Class Intervals and Frequencies
The given class intervals and their frequencies are:
| Class | Frequency |
|--------|-----------|
| 20-29 | 10 |
| 30-39 | 14 |
| 40=49 | 17 |
| 50-59 | 7 |
| 60-69 | 2 |
### Step 2: Cumulative Frequency
To find the cumulative frequency, we sum the frequencies progressively:
- For the interval 20-29: Cumulative frequency is 10.
- For the interval 30-39: Cumulative frequency is [tex]\(10 + 14 = 24\)[/tex].
- For the interval 40=49: Cumulative frequency is [tex]\(24 + 17 = 41\)[/tex].
- For the interval 50-59: Cumulative frequency is [tex]\(41 + 7 = 48\)[/tex].
- For the interval 60-69: Cumulative frequency is [tex]\(48 + 2 = 50\)[/tex].
So, the cumulative frequencies are:
| Class | Cumulative Frequency |
|---------------------- |----------------------|
| Less than or equal to 29 | 10 |
| Less than or equal to 39 | 24 |
| Less than or equal to 49 | 41 |
| Less than or equal to 59 | 48 |
| Less than or equal to 69 | 50 |
### Step 3: Cumulative Relative Frequency
To find the cumulative relative frequency, we divide each cumulative frequency by the total frequency. The total frequency is the sum of all frequencies, which is [tex]\(10 + 14 + 17 + 7 + 2 = 50\)[/tex].
- For the interval 20-29: Cumulative relative frequency is [tex]\(\frac{10}{50} = 0.2\)[/tex].
- For the interval 30-39: Cumulative relative frequency is [tex]\(\frac{24}{50} = 0.48\)[/tex].
- For the interval 40=49: Cumulative relative frequency is [tex]\(\frac{41}{50} = 0.82\)[/tex].
- For the interval 50-59: Cumulative relative frequency is [tex]\(\frac{48}{50} = 0.96\)[/tex].
- For the interval 60-69: Cumulative relative frequency is [tex]\(\frac{50}{50} = 1.0\)[/tex].
So, the cumulative relative frequencies are:
| Class | Cumulative Relative Frequency |
|----------------------- |-------------------------------|
| Less than or equal to 29 | 0.2 |
| Less than or equal to 39 | 0.48 |
| Less than or equal to 49 | 0.82 |
| Less than or equal to 59 | 0.96 |
| Less than or equal to 69 | 1.0 |
Combining both cumulative frequency and cumulative relative frequency distributions:
| Class | Cumulative Frequency | Cumulative Relative Frequency |
|----------------------- |----------------------|-------------------------------|
| Less than or equal to 29 | 10 | 0.2 |
| Less than or equal to 39 | 24 | 0.48 |
| Less than or equal to 49 | 41 | 0.82 |
| Less than or equal to 59 | 48 | 0.96 |
| Less than or equal to 69 | 50 | 1.0 |
These distributions help us understand the accumulation of frequencies and the proportion of the total frequency that falls within or below each class interval.
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
