Following are the number of items of similar type produced in a factory during the last 50 days. 21 22 17 23 27 15 16 
22 15 23 24 25 36 19 14 21 24 25 14 18 20 31 22 19 18 20 21 20 36 18 21 20 31 22 19 18 20 20 24 35 25 26 19 32 22 26 25 
26 27 22 Arrange these observations into a frequency distribution with exclusive class intervals choosing a suitable 
number of classes.

To arrange the given data into a **frequency distribution table** with exclusive class intervals, we will follow these steps:

### Step 1: Find the Range
The range is the difference between the maximum and minimum values in the data.

- Minimum value = 14
- Maximum value = 36

Range = Maximum value - Minimum value = \( 36 - 14 = 22 \)

### Step 2: Decide the Number of Classes
A general rule for the number of classes (\(k\)) is to use Sturges' formula:

\[
k = 1 + 3.322 \log n
\]
where \(n\) is the number of observations.

Given that there are 50 observations, 

\[
k = 1 + 3.322 \log(50) \approx 1 + 3.322 \times 1.6990 \approx 6.64 \approx 7 \text{ classes}
\]

We will create 7 classes.

### Step 3: Determine Class Width
The class width (\(W\)) can be calculated as:

\[
W = \frac{\text{Range}}{\text{Number of Classes}} = \frac{22}{7} \approx 3.14
\]

We round up the class width to 4.

### Step 4: Set Up the Class Intervals
Starting from the minimum value (14), we create the class intervals with a width of 4.

The exclusive intervals would be:
- 14 - 17
- 18 - 21
- 22 - 25
- 26 - 29
- 30 - 33
- 34 - 37

### Step 5: Tally the Frequency

| Class Interval | Frequency |
|----------------|-----------|
| 14 - 17        | 6         |
| 18 - 21        | 13        |
| 22 - 25        | 15        |
| 26 - 29        | 7         |
| 30 - 33        | 4         |
| 34 - 37        | 5         |

### Frequency Distribution Table:
| Class Interval | Frequency | 
|----------------|-----------|
| 14 - 17        | 6         | 
| 18 - 21        | 13        | 
| 22 - 25        | 15        | 
| 26 - 29        | 7         | 
| 30 - 33        | 4         | 
| 34 - 37        | 5         |

This table shows the frequency distribution of the data using exclusive class intervals.

Do you want more details or have any questions?

Here are 5 relative questions to explore further:
1. How do you determine the best number of classes for a distribution?
2. What are inclusive and exclusive class intervals, and how are they different?
3. How would the distribution change with different class widths?
4. How can you create a histogram from this frequency distribution?
5. What are the advantages of frequency distributions in data analysis?

**Tip:** When rounding class widths, always round up to ensure that all data points are included in the intervals.

Following are the number of items of similar type produced in a factory during the last 50 days. 21 22 17 23 27 15 16 22 15 23 24 25 36 19 14 21 24 25 14 18 20 31 22 19 18 20 21 20 36 18 21 20 31 22 19 18 20 20 24 35 25 26 19 32 22 26 25 26 27 22 Arrange these observations into a frequency distribution with exclusive class intervals choosing a suitable number of classes.

Learn how to create a frequency distribution table using exclusive class intervals for factory production data from the last 50 days. This tutorial covers essential statistical concepts, including calculating range, determining class width using Sturges' formula, and organizing data into a frequency table. Suitable for students in Grades 9-12.

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