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When analyzing data, especially with a small sample size like our test of 10 stopping distances, we need to be vigilant about outliers. An outlier is a data point that differs significantly from other observations. Here, the value 102 feet stands out starkly from the rest of the data, as it is much lower.

Managing outliers is crucial as they can skew the results and lead to incorrect conclusions. There are a few common practices for handling outliers:

• Examine the data to ensure there's no error.
• Use statistical methods that are resistant to outliers, like the median.
• Consider removing the outlier if it's due to a data collection error, but be cautious; removing them can sometimes hide important information.

In our exercise, rather than removing the outlier, we used the median as it gives a more accurate reflection of the typical stopping distance when data has an outlier.

A confidence interval provides a range of values that likely contain a population parameter, like the average stopping distance. It helps in understanding the certainty or uncertainty of the measurement.

To construct a confidence interval, you need:

• The sample mean (average), which we calculated as 126.2 feet.
• The standard deviation of the sample, a measure of data dispersion.
• The sample size, which is 10 in this case.

Using the sample statistics, a confidence interval can be calculated to determine if the tires meet the braking requirement of 125 feet. However, our analysis suggested the need to contrast with the median, which, at 128 feet, indicates the tires exceed the expected performance limit. This showcases why using interval estimation is essential for decision-making as it considers variability and uncertainty.

The median is an effective measure of central tendency, especially useful when dealing with skewed data or outliers. By arranging all stopping distances in order and identifying the middle point (or average of middle points), we get a value that represents the center without being influenced by extreme values.

Here, after arranging the stopping distances: 102, 123, 125, 128, 128, 129, 130, 130, 132, and 135, the median is the average of the two middle numbers, 128 and 128, resulting in 128 feet. This is important because it shows that more than half of the stopping distances are indeed above 125 feet, the target set by the company.

Calculating the median in this way helps provide clarity when the data set includes anomalies, giving a more robust way to measure the typical result when compared to the mean.