Construct a frequency distribution table from the following cumulative frequency distribution :
`{:("Calss Interval","Frequency"),(5-10,18),(10-15,30),(15-20,46),(20-25,73),(25-30,90):}`

Answer

To construct a frequency distribution table from the given cumulative frequency distribution, we will follow these steps:

### Step 1: Write down the class intervals and cumulative frequencies
We have the following class intervals and their corresponding cumulative frequencies:

| Class Interval | Cumulative Frequency (CF) |
|----------------|----------------------------|
| 5 - 10 | 18 |
| 10 - 15 | 30 |
| 15 - 20 | 46 |
| 20 - 25 | 73 |
| 25 - 30 | 90 |

### Step 2: Calculate the frequency for each class interval
To find the frequency (F) for each class interval, we will subtract the cumulative frequency of the previous class from the cumulative frequency of the current class.

- For the first class interval (5 - 10):
- Frequency (F) = Cumulative Frequency (CF) = 18

- For the second class interval (10 - 15):
- Frequency (F) = CF (10 - 15) - CF (5 - 10) = 30 - 18 = 12

- For the third class interval (15 - 20):
- Frequency (F) = CF (15 - 20) - CF (10 - 15) = 46 - 30 = 16

- For the fourth class interval (20 - 25):
- Frequency (F) = CF (20 - 25) - CF (15 - 20) = 73 - 46 = 27

- For the fifth class interval (25 - 30):
- Frequency (F) = CF (25 - 30) - CF (20 - 25) = 90 - 73 = 17

### Step 3: Construct the frequency distribution table
Now we can compile the class intervals and their corresponding frequencies into a frequency distribution table:

| Class Interval | Frequency (F) |
|----------------|----------------|
| 5 - 10 | 18 |
| 10 - 15 | 12 |
| 15 - 20 | 16 |
| 20 - 25 | 27 |
| 25 - 30 | 17 |

### Step 4: Verify the frequencies
To ensure that our frequencies are correct, we can sum all the frequencies and check if it matches the last cumulative frequency:

- Total Frequency = 18 + 12 + 16 + 27 + 17 = 90

Since the total frequency equals the last cumulative frequency (90), our calculations are verified.

### Final Frequency Distribution Table:
| Class Interval | Frequency (F) |
|----------------|----------------|
| 5 - 10 | 18 |
| 10 - 15 | 12 |
| 15 - 20 | 16 |
| 20 - 25 | 27 |
| 25 - 30 | 17 |

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