Well, it just goes to show
Sometimes short articles with summary statistics can provide good examples for the three basic interpretations of average: mean, median and mode. This article with results of a survey of people attending the 1996 Royal Hobart Show can be used to discuss all three with a bit of speculation. The claim that 88% enjoyed themselves represents the modal response to a question about whether patrons enjoyed themselves or not. Students can be asked how they know this is an example of a mode (because the percentage is greater than 50% it must be the largest and hence the "enjoyed myself" category must have been the mode).
The claims that the average stay was four hours leads to the belief that this average is either again a mode (if people were given boxes to tick for length of stay) or perhaps the median (if people were asked to state the number of hours they stayed and four was the middle value when all times were ordered). Students could be asked to explain why it is unlikely, although not impossible, that four hours represents the mean stay (because the arithmetic mean would probably not be exactly four but a decimal value like 3.37 or 4.56).
Although not provided in the short piece it is possible for students to calculate the arithmetic mean to find an approximate average amount of money spent at the show ($2,000,000 / 72,000 = $27.78 per person).
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Student Questions for this article
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