Suppose that a customer is purchasing a car.  He conducts an experiment in which he puts 10 gallons of gas in the car and drives it until it runs out of gas. He conducts this experiment 15 times on each car and records the number of miles driven. Car 1	Car 2
214	213
249	201
241	224
242	232
219	252
260	245
251	240
164	286
288	250
251	264
164	291
309	243
276	256
310	268
274	289

It looks like we have a dataset for two cars, where a customer measures the mileage after filling 10 gallons of gas in the car and driving until it runs out of fuel. This experiment is repeated 15 times for each car, and the number of miles driven is recorded.

Let's break down the dataIt looks like we have a dataset for two cars, where a customer measures the mileage after filling 10 gallons of gas in the car and driving until it runs out of fuel. This experiment is repeated 15 times for each car, and the number of miles driven is recorded.

Let's break down the 

**Car 1 (miles driven):**
214, 249, 241, 242, 219, 260, 251, 164, 288, 251, 164, 309, 276, 310, 274

**Car 2 (miles driven):**
213, 201, 224, 232, 252, 245, 240, 286, 250, 264, 291, 243, 256, 268, 289

### To analyze this data, let's compute the following:
1. **Mean mileage** (average miles driven) for both cars.
2. **Variance and standard deviation**, which gives us an idea of the spread or variability in the mileage.
3. **Range** (the difference between the highest and lowest mileage).
4. **Comparison** between the two cars to determine which car is more fuel-efficient on average and which one has more consistent performance.

I'll calculate these metrics now.Here are the key statistics for both cars based on the data provided:

### Car 1:
- **Mean mileage**: 247.47 miles
- **Standard deviation**: 43.90 miles (indicating the spread of values from the mean)
- **Range**: 146 miles (difference between the highest and lowest mileage)

### Car 2:
- **Mean mileage**: 250.27 miles
- **Standard deviation**: 26.73 miles
- **Range**: 90 miles

### Comparison:
- **Average Mileage**: Car 2 has a slightly higher average mileage than Car 1, but the difference is quite small (250.27 vs. 247.47 miles).
- **Consistency**: Car 2 has a much lower standard deviation (26.73 miles) compared to Car 1 (43.90 miles), meaning that Car 2’s mileage is more consistent across trials.
- **Range**: Car 1 has a wider range of values (146 miles) compared to Car 2 (90 miles), which suggests Car 1's mileage varies more.

Do you want further details or have any questions?

Here are five related questions:
1. What does the variance tell us about the performance of each car?
2. How can we interpret the range in relation to driving conditions?
3. Which car might be more reliable based on consistency of performance?
4. Could extreme values (like outliers) affect the decision on which car to choose?
5. How would additional trials affect these statistics?

**Tip**: Standard deviation is a key indicator of consistency; lower values mean more stable performance.

Suppose that a customer is purchasing a car. He conducts an experiment in which he puts 10 gallons of gas in the car and drives it until it runs out of gas. He conducts this experiment 15 times on each car and records the number of miles driven for Car 1 and Car 2.

Analyze the mileage performance of Car 1 and Car 2 by calculating the mean, standard deviation, and range based on 15 trials of driving until the gas runs out. Learn how Car 2 shows more consistent performance despite similar average mileage. Suitable for students in Grades 10-12.

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