Use 

88​-point 

bins 

​(9292 

to 

9999​, 

8484 

to 

9191​, 

​etc.) to make a frequency table for the data set below. Include columns for relative frequency and cumulative frequency.

6868

8383

7171

8181

7373

7575

8989

9898

8080

6868
 
7474

8787

7474

7979

9090

6868

7979

9898

9898

7474

Question content area bottom

Part 1

Complete the table.

​(Type integers or decimals rounded to the nearest tenth as​ needed.)

Data

Frequency

Relative frequency

Cumulative frequency

9292 

to 9999

33

15.015.0​%

enter your response here

Let's build the frequency table using the specified 88-point bins (9292 to 9999, 8484 to 9191, etc.), and calculate the frequency, relative frequency, and cumulative frequency for each bin.

### Step 1: Define Bins
1. **9292 to 9999**
2. **8484 to 9191**
3. **7676 to 8383**
4. **6868 to 7575**

### Step 2: Count Frequencies for Each Bin
To complete this, count how many values fall into each bin.

#### Given Data Set:
\[6868, 8383, 7171, 8181, 7373, 7575, 8989, 9898, 8080, 6868, 7474, 8787, 7474, 7979, 9090, 6868, 7979, 9898, 9898, 7474\]

#### Bin Counts:
1. **9292 to 9999:** 3 values (9898, 9898, 9898)
2. **8484 to 9191:** 3 values (8989, 9090, 8787)
3. **7676 to 8383:** 4 values (8383, 8181, 8080, 7979)
4. **6868 to 7575:** 10 values (6868, 7171, 7373, 7575, 6868, 7474, 7474, 6868, 7979, 7474)

#### Frequencies Summary
- **9292 to 9999:** 3
- **8484 to 9191:** 3
- **7676 to 8383:** 4
- **6868 to 7575:** 10

### Step 3: Relative Frequency Calculation
Relative frequency = \(\frac{\text{Frequency}}{\text{Total Count}}\)

Total Count = 20.

1. **9292 to 9999:** \(\frac{3}{20} = 0.15\) (15%)
2. **8484 to 9191:** \(\frac{3}{20} = 0.15\) (15%)
3. **7676 to 8383:** \(\frac{4}{20} = 0.20\) (20%)
4. **6868 to 7575:** \(\frac{10}{20} = 0.50\) (50%)

### Step 4: Cumulative Frequency Calculation
Cumulative frequency is the running total of the frequencies.

1. **9292 to 9999:** 3
2. **8484 to 9191:** 3 + 3 = 6
3. **7676 to 8383:** 6 + 4 = 10
4. **6868 to 7575:** 10 + 10 = 20

### Completed Table

| Data Range    | Frequency | Relative Frequency | Cumulative Frequency |
|---------------|-----------|--------------------|-----------------------|
| 9292 to 9999  | 3         | 15.0%             | 3                     |
| 8484 to 9191  | 3         | 15.0%             | 6                     |
| 7676 to 8383  | 4         | 20.0%             | 10                    |
| 6868 to 7575  | 10        | 50.0%             | 20                    |

Would you like further details on any of the steps?

---

### Follow-up Questions
1. How is cumulative frequency used in data analysis?
2. How can relative frequency help compare different data sets?
3. How would the table change if we used smaller bin sizes?
4. Why is it important to round percentages to a consistent decimal place?
5. How can frequency tables help identify data trends?

**Tip:** When constructing bins, ensure that each data point is only included in one bin to avoid overlap errors.

Use 88-point bins (9292 to 9999, 8484 to 9191, etc.) to make a frequency table for the data set below. Include columns for relative frequency and cumulative frequency.

6868, 8383, 7171, 8181, 7373, 7575, 8989, 9898, 8080, 6868, 7474, 8787, 7474, 7979, 9090, 6868, 7979, 9898, 9898, 7474

Complete the table.

Learn how to construct a frequency table using 88-point bins (e.g., 9292 to 9999, 8484 to 9191) for a given data set. This problem covers key statistical concepts like frequency distribution, relative frequency, and cumulative frequency. Suitable for students in Grades 9-11.

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