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The image you've uploaded contains a problem about petrol amounts bought by customers at a service station, given in liters, along with several questions related to estimating the mean using class intervals.

Let's go through the problem step by step:

### Problem Breakdown:
1. **Given Data**: A list of petrol amounts bought by customers during one hour.
2. **Questions**:
   - **a**: Calculate the actual mean \( \bar{p} \) of the data.
   - **b(i)**: Organize the data into specific class intervals and estimate the mean.
   - **b(ii)**: Use these intervals to estimate the mean of the data.
   - **c(i)**: Organize the data into different class intervals and estimate the mean.
   - **c(ii)**: Use these intervals to estimate the mean.
   - **d**: Compare the estimates from **b** and **c** with the actual mean found in **a**.
   - **e**: Discuss whether larger or smaller intervals would produce a more accurate estimate of the mean.

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Let's start with **part (a)** by calculating the mean of the given data.

### Petrol Amounts (liters):
41.59, 33.09, 37.21, 58.85, 47.20, 26.01, 31.12, 41.11, 56.21, 23.46,  
31.77, 44.56, 23.15, 46.67, 44.35, 43.12, 22.09, 47.62, 43.76, 27.56,  
28.90, 36.82, 47.17, 38.18, 45.90, 43.94, 39.72, 43.23, 44.42, 26.91,  
46.12, 27.09, 57.85, 33.13, 51.03, 45.92, 52.79, 44.18, 51.14, 50.53,  
37.10, 52.39, 48.52, 41.08, 22.09, 49.91, 38.10, 58.72, 25.87, 49.90.

We will first calculate the mean of these values.

Let me do the calculations.The mean amount of petrol bought by customers, \( \bar{p} \), is approximately **40.98 liters**.

Now, let's proceed to part **b** of the question, where we need to organize the data into class intervals and estimate the mean. The given intervals are:

- \( 20 \leq p < 30 \)
- \( 30 \leq p < 40 \)
- \( 40 \leq p < 50 \)
- \( 50 \leq p < 60 \)

I'll organize the data into these intervals and estimate the mean using a frequency table. Let me calculate that.It seems like I can’t do more advanced data analysis right now. Please try again later.

In the meantime, you can organize the data into the provided class intervals manually. Here's a brief outline of how to do it:

### Steps to Estimate the Mean for Part **b(i)**:
1. Organize the data into the class intervals:
   - \( 20 \leq p < 30 \)
   - \( 30 \leq p < 40 \)
   - \( 40 \leq p < 50 \)
   - \( 50 \leq p < 60 \)

2. For each interval, count how many data points fall within it.

3. Find the midpoint of each interval, which is the average of the lower and upper bounds.

4. Multiply the frequency (number of data points) for each class by its midpoint.

5. Sum these values and divide by the total number of data points to estimate the mean.

If you'd like, I can guide you through the process or help with another part of the problem.

Do you want to proceed with this or have any specific questions?

Here are 5 related questions you might want to explore:
1. How do class intervals affect the accuracy of mean estimates?
2. What are the advantages of using smaller class intervals?
3. How is the midpoint chosen for class intervals?
4. What factors should be considered when selecting interval sizes?
5. How does grouping data affect statistical calculations like variance?

**Tip**: When estimating means from grouped data, always check the number of intervals to avoid overgeneralization.

The amounts of petrol bought in one hour by customers at a service station are shown, in litres. Find the actual mean, estimate the mean using class intervals, and compare estimates.

Learn how to calculate the mean of petrol amounts bought by customers at a service station and estimate the mean using grouped class intervals. This problem covers statistical concepts such as mean, class intervals, and grouped data, suitable for students in Grades 10-12.

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