n a survey of 20 patients who smoked, the following data were obtained. Each value
represents the number of cigarettes the patient smoked per day. Construct a frequency
distribution, using six classes.
10, 8, 6, 14
22, 13, 17, 19
11, 9, 18, 14
13, 12, 15, 15
5, 11, 16, 11

To construct a frequency distribution with six classes, we follow these steps:

### Step 1: Organize the data.
The data (number of cigarettes smoked per day) is:
\[
10, 8, 6, 14, 22, 13, 17, 19, 11, 9, 18, 14, 13, 12, 15, 15, 5, 11, 16, 11
\]

### Step 2: Identify the range.
The range is the difference between the largest and smallest values.
\[
\text{Range} = \text{Max value} - \text{Min value} = 22 - 5 = 17
\]

### Step 3: Determine the class width.
To determine the class width, divide the range by the number of classes, then round up to the nearest whole number.
\[
\text{Class width} = \frac{\text{Range}}{\text{Number of classes}} = \frac{17}{6} \approx 2.83 \Rightarrow 3
\]

### Step 4: Create the class limits.
Start with the smallest value (5), and increment by the class width (3):
- Class 1: 5 – 7
- Class 2: 8 – 10
- Class 3: 11 – 13
- Class 4: 14 – 16
- Class 5: 17 – 19
- Class 6: 20 – 22

### Step 5: Tally the frequencies.
Now, count how many values fall into each class:

| Class    | Range    | Frequency |
|----------|----------|-----------|
| Class 1  | 5 – 7    | 2         |
| Class 2  | 8 – 10   | 3         |
| Class 3  | 11 – 13  | 6         |
| Class 4  | 14 – 16  | 6         |
| Class 5  | 17 – 19  | 3         |
| Class 6  | 20 – 22  | 1         |

Thus, the frequency distribution is:

| **Class** | **Range** | **Frequency** |
|-----------|-----------|---------------|
| 1         | 5 – 7     | 2             |
| 2         | 8 – 10    | 3             |
| 3         | 11 – 13   | 6             |
| 4         | 14 – 16   | 6             |
| 5         | 17 – 19   | 3             |
| 6         | 20 – 22   | 1             |

Would you like me to explain the steps in more detail or assist you with any other questions? 

Here are some related questions:
1. How do you calculate cumulative frequency from this distribution?
2. How can you draw a histogram from this frequency distribution?
3. What is the relative frequency, and how can it be added to the table?
4. How does this data compare to a normal distribution?
5. How can you determine the median from this frequency distribution?

**Tip:** Always ensure your class intervals cover the full range of data, with no gaps or overlaps.

In a survey of 20 patients who smoked, the following data were obtained. Each value represents the number of cigarettes the patient smoked per day. Construct a frequency distribution, using six classes. 10, 8, 6, 14, 22, 13, 17, 19, 11, 9, 18, 14, 13, 12, 15, 15, 5, 11, 16, 11

Learn how to construct a frequency distribution for the number of cigarettes smoked per day by 20 patients. The data includes values such as 10, 8, 6, and 22, and the steps involve calculating the range, class width, and tallying frequencies into six classes. Suitable for students in Grades 9-11.

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