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Part 1

Use 

55​-point 

bins 

​(95 to 9995 to 99​, 

90 to 9490 to 94​, 

​etc.) to make a frequency table for the set of exam scores shown below. Include columns for relative frequency and cumulative frequency. 

7676  

8787  

8383  

7878  

9191  

7575  

9999  

8686  

8383  

9595  

7070  

8585  

9393  

7575  

9090  

9191  

9393  

8080  

8989  

8787 
  
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Part 1

Complete the frequency table below.

**Scores**

**Frequency**

**Relative Frequency**

**Cumulative Frequency**

95 to 9995 to 99

enter your response here

enter your response here​%

enter your response here

Let's work through the problem step-by-step.

We have a list of exam scores, and we're instructed to create a frequency table using 5-point bins, starting from the 90-94 range and moving upwards.

### Given Scores:
76, 87, 83, 78, 91, 75, 99, 86, 83, 95, 70, 85, 93, 75, 90, 91, 93, 80, 89, 87

### Bins:
- 95 to 99
- 90 to 94
- 85 to 89
- 80 to 84
- 75 to 79
- 70 to 74

### Steps to Create the Frequency Table:
1. **Frequency**: Count how many scores fall into each bin.
2. **Relative Frequency**: Divide the frequency of each bin by the total number of scores, then multiply by 100 to convert to a percentage.
3. **Cumulative Frequency**: Add the frequencies in a running total from the lowest bin to the highest.

#### 1. Frequency Count:
We count the scores falling into each bin:
- **95 to 99**: 99, 95 → 2 scores
- **90 to 94**: 91, 93, 91, 93, 90 → 5 scores
- **85 to 89**: 87, 86, 85, 87, 89 → 5 scores
- **80 to 84**: 83, 83, 80 → 3 scores
- **75 to 79**: 76, 78, 75, 75 → 4 scores
- **70 to 74**: 70 → 1 score

#### 2. Relative Frequency:
Total number of scores = 20

For each bin:
- **95 to 99**: (2/20) * 100 = 10%
- **90 to 94**: (5/20) * 100 = 25%
- **85 to 89**: (5/20) * 100 = 25%
- **80 to 84**: (3/20) * 100 = 15%
- **75 to 79**: (4/20) * 100 = 20%
- **70 to 74**: (1/20) * 100 = 5%

#### 3. Cumulative Frequency:
- **95 to 99**: 2
- **90 to 94**: 2 + 5 = 7
- **85 to 89**: 7 + 5 = 12
- **80 to 84**: 12 + 3 = 15
- **75 to 79**: 15 + 4 = 19
- **70 to 74**: 19 + 1 = 20

### Completed Frequency Table:

| **Scores**  | **Frequency** | **Relative Frequency** | **Cumulative Frequency** |
|-------------|---------------|------------------------|--------------------------|
| 95 to 99    | 2             | 10%                    | 2                        |
| 90 to 94    | 5             | 25%                    | 7                        |
| 85 to 89    | 5             | 25%                    | 12                       |
| 80 to 84    | 3             | 15%                    | 15                       |
| 75 to 79    | 4             | 20%                    | 19                       |
| 70 to 74    | 1             | 5%                     | 20                       |

---

Would you like more details or any further clarifications?

### Related Questions:
1. How would the table change if we used different bin sizes (e.g., 10-point bins)?
2. What is the importance of cumulative frequency in understanding data distribution?
3. How does the choice of bin size affect the relative frequency distribution?
4. Can you create a histogram based on this frequency table?
5. What additional insights can we gain by analyzing the median or mode of this data?

### Tip:
The cumulative frequency helps to quickly see how data accumulates across ranges, which is useful for percentile calculations.

Use 5-point bins (95 to 99, 90 to 94, etc.) to make a frequency table for the set of exam scores shown below. Include columns for relative frequency and cumulative frequency.

Scores:
76, 87, 83, 78, 91, 75, 99, 86, 83, 95, 70, 85, 93, 75, 90, 91, 93, 80, 89, 87.

Learn how to create a frequency table using 5-point bins for a given set of exam scores. This problem includes frequency, relative frequency, and cumulative frequency calculations. Explore how to group data and analyze its distribution. Perfect for students in Grades 9-12 studying basic statistics.

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