To construct a frequency distribution with 5 classes, let's break down the process step by step.

1. Data Overview

The data points are: 1, 29, 23, 14, 14, 10, 27, 16, 13, 21, 27, 24, 17, 20, 16, 0, 23, 22, 18, 12

2. Range of Data

• Minimum value: 0
• Maximum value: 29

3. Class Width Calculation

To determine the class width, we can use the formula: $\text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}}$ $\text{Class Width} = \frac{29 - 0}{5} = \frac{29}{5} \approx 5.8 \approx 6 \text{ (rounded up to nearest whole number)}$

4. Class Limits and Frequency Distribution

Now, we define the 5 classes, calculate frequencies, midpoints, relative frequencies, and cumulative frequencies.

Class 1:

• Class = 0 to 5
• Frequency = 2 (Data points: 0, 1)
• Midpoint = $\frac{0 + 5}{2} = 2.5$
• Relative Frequency = $\frac{2}{20} = 0.10$
• Cumulative Frequency = 2

Class 2:

• Class = 6 to 11
• Frequency = 3 (Data points: 10, 12, 10)
• Midpoint = $\frac{6 + 11}{2} = 8.5$
• Relative Frequency = $\frac{3}{20} = 0.15$
• Cumulative Frequency = 2 + 3 = 5

Class 3:

• Class = 12 to 17
• Frequency = 8 (Data points: 14, 14, 16, 13, 16, 17, 12)
• Midpoint = $\frac{12 + 17}{2} = 14.5$
• Relative Frequency = $\frac{8}{20} = 0.40$
• Cumulative Frequency = 5 + 8 = 13

Class 4:

• Class = 18 to 23
• Frequency = 6 (Data points: 18, 20, 21, 22, 23, 23)
• Midpoint = $\frac{18 + 23}{2} = 20.5$
• Relative Frequency = $\frac{6}{20} = 0.30$
• Cumulative Frequency = 13 + 6 = 19

Class 5:

• Class = 24 to 29
• Frequency = 4 (Data points: 24, 27, 27, 29)
• Midpoint = $\frac{24 + 29}{2} = 26.5$
• Relative Frequency = $\frac{4}{20} = 0.20$
• Cumulative Frequency = 19 + 4 = 20

Summary Table

Class	Frequency	Midpoint	Relative Frequency	Cumulative Frequency
0 to 5	2	2.5	0.10	2
6 to 11	3	8.5	0.15	5
12 to 17	8	14.5	0.40	13
18 to 23	6	20.5	0.30	19
24 to 29	4	26.5	0.20	20

Would you like more details or have any questions?

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Here are 5 related questions:

1. How would the frequency distribution change if the data included a new entry of 30?
2. Can you calculate the cumulative relative frequency for each class?
3. What would the distribution look like if we used 6 classes instead of 5?
4. How does the midpoint help in understanding the frequency distribution?
5. What is the significance of the relative frequency in interpreting the data?

Tip: Always ensure that the sum of the relative frequencies equals 1, as it represents the entire dataset.