https://file.aiquickdraw.com/mathbot/file/1724142029523kczujgpb.jpg

Data menunjukkan bilangan kereta yang mengalami kemalangan dalam sebuah bandar besar untuk tempoh 30 hari. Dengan menggunakan Sturges’ Rule, tentukan bilangan kelas, julat dan selang kelas bagi data di atas.

To determine the number of classes, range, and class interval for the given data using Sturges' Rule, we'll follow these steps:

1. **Compile the data**: First, we'll extract the numbers from the image.
2. **Calculate the Range (R)**: The range is the difference between the maximum and minimum values in the data.
3. **Determine the Number of Classes (k)**: Using Sturges' Rule, the formula is \( k = 1 + 3.322 \log_{10}(n) \), where \( n \) is the number of data points.
4. **Calculate the Class Interval (h)**: The class interval is given by \( h = \frac{R}{k} \).

### Step 1: Compile the Data
From the image, the data set is:

\[
73, 66, 78, 53, 52, 38, 61, 66, 80, 79, 51, 54, 65, 69, 51, 69, 57, 60, 58, 76, 76, 56, 59, 72, 57, 70, 61, 54, 51, 63
\]

### Step 2: Calculate the Range (R)
- Maximum value (\( \text{Max} \)) = 80
- Minimum value (\( \text{Min} \)) = 38

\[
R = \text{Max} - \text{Min} = 80 - 38 = 42
\]

### Step 3: Determine the Number of Classes (k)
- Number of data points (\( n \)) = 30

Using Sturges' Rule:

\[
k = 1 + 3.322 \log_{10}(30)
\]

I'll calculate this now.

### Step 4: Calculate the Class Interval (h)
Once we have \( k \), the class interval \( h \) is calculated as:

\[
h = \frac{R}{k}
\]

Let me calculate these values.Here are the results:

1. **Range (R)**: The range of the data is 42.
2. **Number of Classes (k)**: According to Sturges' Rule, the number of classes should be approximately 5.91, which we typically round up to 6.
3. **Class Interval (h)**: The class interval is approximately 7.11.

So, you would typically use 6 classes with a class interval of about 7 units to represent this data.

Would you like more details or have any questions? Here are some related questions you might find helpful:

1. How do you construct a frequency distribution table with the given class interval?
2. What are the implications of using a different rule instead of Sturges' Rule for determining the number of classes?
3. How does the class interval affect the interpretation of the data in a histogram?
4. Could you explain how to calculate the logarithm used in Sturges' Rule?
5. How would the results change if the data set were significantly larger or smaller?

**Tip**: When rounding the number of classes, it's often practical to round up to ensure that the data is well-distributed across the classes.

Learn how to use Sturges' Rule to determine the number of classes, range, and class interval for accident data over a 30-day period in a large city. Includes step-by-step calculations and implications of using Sturges' Rule in statistics.

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