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Analyzing Visitor Distances: A Statistics Case Study

This case study explores a practical statistics problem involving a museum's visitor data. With insights gathered from 33,000 visitors, the task is to construct a histogram to visualize the travel distance of guests and calculate how many in a stratified sample of 100 traveled more than five miles to the museum. Common pitfalls include confusing histograms with bar charts and careless calculation errors. This scenario not only showcases data handling skills but also highlights the importance of clear statistical representation and accurate methods in analysis.

armando-sykes
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Analyzing Visitor Distances: A Statistics Case Study

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  1. Functional Question Higher (Statistics 9) For the week beginning ….

  2. The owner of a museum wants to know the distance that visitors travel to the museum.  Information is collected from 33 000 visitors. The table shows this information. (a)     Construct a histogram on the grid below to show this information. (3) (b)     A stratified sample of 100 is taken from these 33 000 visitors.           Calculate the number in the sample who travel more than five miles. Answer ................................................ (2) (Total 5 marks)

  3. Common Mistakes – what did the examiners say? The histogram in part (a) was well done by a number of candidates yet just over half scored zero often because they had simply drawn a bar chart. The fact that a bar chart either went over the top of the available graph paper or only filled just over half of the graph paper depending on the scale chosen did not seem to deter candidates. Some very good candidates produced all the necessary calculations but sadly made careless mistakes when using their scales, including going beyond 100 on the horizontal scale.           In part (b), those who did use a correct method, frequently chose inefficient ways to obtain an answer, often preferring to find each of the three largest groups sample sizes and adding them together, rather than finding the sample size for 5 miles of less and subtracting from one hundred.

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