The data represent the time, in minutes, spent reading a political blog in a day. Construct a frequency distribution using 5 classes. In the table, include the midpoints, relative frequencies, and cumulative frequencies.

(1 29 23 14) (14 10 27 16) (13 21 27 24) (17 20 16 0) (23 22 18 12)

Fill in the blanks, starting with the lowest class limit.

Class = _ to _
Frequency = _
Midpoint = _
Relative frequency = _
Cumulative frequency = _

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?

---

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.

Learn how to construct a frequency distribution using 5 classes based on given data points. This problem involves calculating class widths, determining class limits, and computing midpoints, relative frequencies, and cumulative frequencies. Suitable for high school students learning statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation