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
Is your distribution normal or skewed? If skewed, what direction is the skew?
Does "appropriate" mean the most representative or the one that makes the tire wear look best?
normal
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 and the goal of the campaign.
There are three common types of statistical averages: the mean, the median, and the mode.
1. Mean: The mean is calculated by summing up all the values and dividing by the total number of values. It represents the average value of the data set.
2. Median: The median is the middle value of a data set when it is sorted in ascending or descending order. It divides the data into two equal halves, with 50% of the values being greater and 50% being smaller.
3. Mode: The mode represents the most frequently occurring value in a dataset.
In this case, we need to determine which average is the most appropriate for describing the 'average' tyre life in an advertising campaign.
If we assume that the goal of the advertising campaign is to showcase the typical lifespan of the tyres, then the statistical average that takes into account the whole range of values would be most appropriate. In this case, the mean would be the most suitable choice.
To calculate the mean, you would sum up all the values and divide by the total number of values (48 in this case). For example:
Mean = (value1 + value2 + ... + value48) / 48
Once you have the mean, you can use it in the advertising campaign to provide an overall representation of the 'average' tyre life from the sample.
It is important to note that other statistical measures, such as the median or mode, could provide additional information about the distribution of the data. However, for an advertising campaign, it is often more relevant to provide a single number that represents the 'average' tyre life.