https://file.aiquickdraw.com/mathbot/file/1725447009439tv0njtwz.jpg

Let's calculate the mean prices for both Ballarat and Ararat. 

### Step 1: List the prices for each location.

**Ballarat:**
- 145.9
- 152.8
- 141.3
- 165.9
- 161.8

**Ararat:**
- 165.2
- 161.9
- 170.5
- 168.2
- 171.3

### Step 2: Calculate the mean (average) for each location.

The formula for the mean is:

\[
\bar{x} = \frac{\text{Sum of all values}}{\text{Number of values}}
\]

#### For Ballarat:

\[
\bar{x}_{\text{Ballarat}} = \frac{145.9 + 152.8 + 141.3 + 165.9 + 161.8}{5}
\]

#### For Ararat:

\[
\bar{x}_{\text{Ararat}} = \frac{165.2 + 161.9 + 170.5 + 168.2 + 171.3}{5}
\]

Let's calculate these.

### Step 3: Perform the calculations.

#### Ballarat:
\[
\bar{x}_{\text{Ballarat}} = \frac{145.9 + 152.8 + 141.3 + 165.9 + 161.8}{5} = \frac{767.7}{5} = 153.54
\]

Rounding to 1 decimal place: 
\[
\bar{x}_{\text{Ballarat}} = 153.5
\]

#### Ararat:
\[
\bar{x}_{\text{Ararat}} = \frac{165.2 + 161.9 + 170.5 + 168.2 + 171.3}{5} = \frac{837.1}{5} = 167.42
\]

Rounding to 1 decimal place:
\[
\bar{x}_{\text{Ararat}} = 167.4
\]

### Final Answer:
- **Ballarat Mean Price:** 153.5 cents
- **Ararat Mean Price:** 167.4 cents

Would you like more details or have any questions?

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Here are 5 relative questions you might consider:
1. How is the median price calculated, and how does it compare to the mean in this context?
2. What is the range of petrol prices in Ballarat and Ararat?
3. How would removing the highest or lowest price affect the mean in each location?
4. Can the mean be misleading in certain datasets, and if so, why?
5. How does the variance or standard deviation of the prices provide additional insight?

**Tip:** When comparing two datasets, calculating both the mean and median can provide a clearer picture of the central tendency and potential outliers.

Find the mean petrol prices for Ballarat and Ararat, given the prices in cents.

Learn how to calculate the mean petrol prices for Ballarat and Ararat using the given data. This problem covers key statistical concepts, such as calculating the arithmetic mean. Suitable for students in Grades 6-8.

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