Form a grouped frequency distribution from the following data by inclusive method taking 4 as the class size of class intervals.
31, 23, 19, 29, 22, 20, 16, 10, 13, 34, 38, 33, 28, 21, 15, 18, 36, 24, 18, 15, 12, 30, 27, 23, 20, 17, 14, 32, 26, 25, 18, 29, 24, 19, 16, 11, 22, 15, 17,10

Answer

To form a grouped frequency distribution using the inclusive method with a class size of 4 from the given data, we will follow these steps:

### Step 1: Arrange the Data in Ascending Order
First, we need to arrange the given data in ascending order.

**Data:**
10, 10, 10, 11, 12, 13, 14, 15, 15, 15, 15, 16, 16, 17, 17, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 23, 24, 24, 25, 26, 26, 27, 28, 29, 29, 30, 31, 32, 33, 34, 36, 38

### Step 2: Determine the Class Intervals
We will create class intervals of size 4. The smallest number in the data is 10, so we will start from 10.

**Class Intervals:**
- 10 - 13
- 14 - 17
- 18 - 21
- 22 - 25
- 26 - 29
- 30 - 33
- 34 - 37
- 38 - 41

### Step 3: Tally the Frequencies
Now, we will count how many data points fall into each class interval.

1. **10 - 13:** 10, 10, 10, 11, 12, 13 (6)
2. **14 - 17:** 14, 15, 15, 15, 15, 16, 16, 17, 17 (9)
3. **18 - 21:** 18, 18, 18, 19, 19, 20, 20, 20, 21, 21 (10)
4. **22 - 25:** 22, 22, 22, 23, 23, 24, 24, 25 (8)
5. **26 - 29:** 26, 26, 27, 28, 29, 29 (6)
6. **30 - 33:** 30, 31, 32, 33 (4)
7. **34 - 37:** 34 (1)
8. **38 - 41:** 38 (1)

### Step 4: Create the Frequency Distribution Table
Now we will summarize the data in a frequency distribution table.

| Class Interval | Tally Marks | Frequency |
|----------------|-------------|-----------|
| 10 - 13 | ||||| ||| | 6 |
| 14 - 17 | ||||| |||| | 9 |
| 18 - 21 | ||||| ||||| | 10 |
| 22 - 25 | ||||| |||| | 8 |
| 26 - 29 | ||||| || | 6 |
| 30 - 33 | ||||| | 4 |
| 34 - 37 | | | 1 |
| 38 - 41 | | | 1 |

### Step 5: Verify the Total Frequency
Finally, we will sum the frequencies to ensure they match the total number of data points.

**Total Frequency:** 6 + 9 + 10 + 8 + 6 + 4 + 1 + 1 = 45