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Using Sturge’s Rule, construct a frequency distribution with a cumulative frequency and upper boundary. 

To construct a frequency distribution using **Sturges' Rule** from the provided data, we'll follow these steps:

### Step 1: Sturges' Rule for Number of Classes
Sturges' Rule helps us determine the number of classes, \( k \), using the formula:
\[
k = 1 + \log_2(n)
\]
Where:
- \( n \) is the number of data points.

Here, \( n = 33 \).

### Step 2: Calculate Class Width
To calculate the class width, we first find the range of the dataTo construct a frequency distribution using **Sturges' Rule** from the provided data, we'll follow these steps:

### Step 1: Sturges' Rule for Number of Classes
Sturges' Rule helps us determine the number of classes, \( k \), using the formula:
\[
k = 1 + \log_2(n)
\]
Where:
- \( n \) is the number of data points.

Here, \( n = 33 \).

### Step 2: Calculate Class Width
To calculate the class width, we first find the range of the 
\[
\text{Range} = \text{Maximum value} - \text{Minimum value}
\]

Then we divide the range by the number of classes to get the class width.

### Step 3: Create the Frequency Distribution
Once we have the number of classes and class width, we can construct the frequency distribution, which includes:
1. Class intervals (based on class width).
2. Frequency for each class.
3. Cumulative frequency.
4. Upper boundary for each class.

I'll now perform the calculations to obtain the required frequency distribution.The frequency distribution using **Sturges' Rule** for the given data is as follows:

| Class Interval | Frequency | Cumulative Frequency |
|----------------|-----------|----------------------|
| 11 - 20        | 5         | 5                    |
| 21 - 30        | 3         | 8                    |
| 31 - 40        | 11        | 19                   |
| 41 - 50        | 6         | 25                   |
| 51 - 60        | 5         | 30                   |
| 61 - 70        | 3         | 33                   |

This table includes the class intervals, frequency of data points in each interval, and the cumulative frequency up to each class.

Would you like a more detailed explanation or any further analysis?

Here are some related questions:
1. How does Sturges' Rule compare to other binning methods for frequency distribution?
2. Can we use a different number of classes for this data, and what impact would it have?
3. How can we visualize this frequency distribution?
4. What is the impact of cumulative frequency on interpreting data trends?
5. How would this frequency distribution change with a larger data set?

**Tip:** When creating class intervals, ensure that the data covers the full range of values without overlap, and adjust the class width to avoid too many or too few classes.

Using Sturge’s Rule, construct a frequency distribution with a cumulative frequency and upper boundary.

This problem involves using Sturges' Rule to construct a frequency distribution for 33 participants' quiz scores. The steps include determining class intervals, frequencies, cumulative frequencies, and calculating the upper boundary.

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