Using the following data: 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7
- What is the mean of these data? Mean = 3.8
- What is the median? Median=4
- What are the mode or modes of these data? There are two modes, 2 and 5
- Are the data provided unimodal, bimodal, trimodal, polymodal or amodal (no mode)? These data are bimodal
- What is the range and interquartile range of these data> The range is 6 IQR is 3
Using the following data: 7.2, 7.5, 7.1, 7.6, 8.2, 7.3, 7.7
- What is the mean of these data? Mean = 7.51
- What is the median? Median = 7.5
- What are the mode or modes of these data? There is no mode
- Are the data provided unimodal, bimodal, trimodal, polymodal or amodal (no mode)? Amodal
- What is the range and interquartile range of these data? Range = 1.1, IQR=0.4
- A politician once famously promised to "raise everyone's wage above the average" in a campaign speech. Is this possible? Explain your answer briefly. No. Consider the case that everyone earns the same - at this point everyone earns the average wage, but no one earns more. If just one person earns a different amount the mean will move towards that. If one person earns a little more than everyone else, then everyone else earns less than average, if one earns a little less everyone else earns a bit more than average - but it is not possible for everyone to earn more than average.
- If you answered yes, give a sample data set (at least 10 elements) to show how this can be possible. If you answered no, if there are 20 million wage earners, what is the minimum number of people who must be below average if everyone else is to earn over average wage? Only 1 person need be below average. In fact, in the UK's wage pattern more than half of the population earn under average wage, because there are a small number of very high earners who drag the average up.
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