A tyre manufacturer has chosen 48 tyres at random from a production line and issued them to taxis

for testing. Assume that the 48 numbers you have selected refer to the number of thousands of
kilometres travelled during the life of each tyre. (For example, a value of ‘32’ represents 32 000 km of
travel.)
Which statistical average would be most appropriate to describe the ‘average’ tyre life in an
advertising campaign? Justify your decision.

To determine the most appropriate statistical average to describe the "average" tyre life in an advertising campaign, we can consider the three common types of averages: mean, median, and mode.

1. Mean: The mean is calculated by summing up all the values and dividing it by the total number of values. It represents the overall average of a set of values.

2. Median: The median is the middle value when the values are arranged in ascending or descending order. It is useful when there are extreme values or outliers in the data, as it is less affected by these values.

3. Mode: The mode is the value that appears most frequently in the data set. It indicates the most common value or value range.

In this case, to describe the "average" tyre life in an advertising campaign, the most appropriate statistical average would be the median. Here's why:

1. Outliers: Since the tyres are randomly selected from a production line, it is possible that some of them may have significantly shorter or longer lives due to various factors. These outliers could skew the mean and make it not representative of the typical tyre life. The median, on the other hand, would be less affected by outliers.

2. Realistic expectation: The median represents the middle value, so it provides a realistic expectation of the typical tyre life. It would be more relatable to consumers who are considering buying the tyres, as it gives them an idea of what they can reasonably expect in terms of durability.

3. Variability: The median is less affected by extreme values or highly variable data, which could be the case with tyre life. Different factors can impact tyre wear, such as driving conditions, maintenance, and individual driving habits. The median would provide a better estimate of the typical tyre life, considering these variables.

Therefore, by using the median as the statistical average, the tyre manufacturer can present a more accurate and reliable representation of the "average" tyre life in their advertising campaign.