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 need to consider the characteristics of the data set and the objective of the campaign.
In this case, we have 48 randomly selected values representing the number of thousands of kilometers traveled by each tyre. These values are likely to vary.
There are three main types of statistical averages: the mean, the median, and the mode.
1. Mean: The mean is calculated by adding up all the values and dividing by the total number of values. It represents the arithmetic average of the data set.
2. Median: The median represents the middle value of the data set when the values are arranged in ascending or descending order. If there is an even number of values, the median is the average of the two middle values.
3. Mode: The mode represents the value that appears most frequently in the data set.
In this case, we need to consider the purpose of the advertising campaign. If the objective is to highlight the typical or representative tyre life, the mean would be the most appropriate statistical average. It provides a comprehensive picture of the average tyre life by taking into account all the values in the data set. However, the mean can be influenced by outliers, which are extreme values that deviate significantly from the rest of the data. If there are extreme values in the data set, they can disproportionately affect the mean.
If the objective is to showcase the most common or typical tyre life experienced by customers, the median or mode might be more appropriate. The median represents the middle value, which is less affected by extreme values. The mode represents the most frequent value, which can provide insight into the most common tyre life experienced.
Ultimately, the choice of statistical average depends on the specific objective of the advertising campaign and the characteristics of the data set. It is important to consider the potential impact of outliers and the desired representation of the average tyre life.