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To determine which firm can claim better performance, we can analyze the data for **Firm A** and **Firm B** using the provided statistical measures: **Mean**, **Median**, and **Range**.

### 1. **Mean:**
   - **Firm A:** 24,800 miles
   - **Firm B:** 24,200 miles

   The mean is the average mileage of tires before rejection. Here, **Firm A** has a higher mean (24,800 miles) compared to **Firm B** (24,200 miles). This suggests that, on average, **Firm A's** tires last longer before rejection.

### 2. **Median:**
   - **Firm A:** 24,600 miles
   - **Firm B:** 25,000 miles

   The median represents the middle value of the data, providing insight into the central tendency of the mileage. Here, **Firm B** has a higher median (25,000 miles) than **Firm A** (24,600 miles). This indicates that more than half of **Firm B's** tires tend to last longer than **Firm A's** tires.

### 3. **Range:**
   - **Firm A:** 4,900 miles
   - **Firm B:** 5,000 miles

   The range gives the difference between the maximum and minimum mileage values, showing the spread of the data. **Firm B** has a slightly larger range (5,000 miles) compared to **Firm A** (4,900 miles), which means that **Firm B's** tire performance varies slightly more.

### Conclusion:
- **Firm A** has a higher mean mileage, implying that, on average, its tires last longer before rejection.
- **Firm B** has a higher median mileage, suggesting that at least 50% of **Firm B's** tires last longer than **Firm A's** tires.
- Both firms have similar ranges, with **Firm B's** performance being slightly more variable.

Given the higher median and a slightly larger range, **Firm B** could argue that more of their tires perform better consistently. However, **Firm A** can claim better average performance based on the mean.

The decision depends on whether consistency (median) or average performance (mean) is valued more.

Would you like a more detailed analysis or have any questions?

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### Follow-up Questions:
1. What is the significance of using mean vs. median when comparing data sets?
2. How can the range affect the interpretation of tire performance data?
3. If the distribution of the mileage data was known, how could it influence the decision?
4. Why might a company prefer a higher median value over a higher mean value?
5. How would an outlier in the mileage data impact the mean, median, and range?

### Tip:
When comparing data, always consider both the central tendency (mean, median) and the spread (range) to get a comprehensive understanding of performance.

Firms A and B both claim that their tires show better performance on the basis of tests held. The results provided are for mileage run by tires before rejection:
- Firm A: Mean = 24,800 miles, Median = 24,600 miles, Range = 4,900 miles
- Firm B: Mean = 24,200 miles, Median = 25,000 miles, Range = 5,000 miles

Can you indicate which of the two firms can claim better performance? Give your reasons.

Analyze and compare the performance of tires from Firm A and Firm B based on statistical measures such as mean, median, and range. Firm A's tires have a higher mean mileage, while Firm B has a higher median and range. Learn how to interpret these statistics and decide which firm can claim better performance.

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