Answer :
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.
