Mean, Median, and an Outlier in Reading Minutes
Ms. Rivera's sixth graders collect weekly reading minutes for nine students. The totals, in minutes, are 20, 25, 25, 30, 30, 35, 35, 40, and 180. One student reports that 'the average is about 46.7 minutes, so a typical student reads about 47 minutes a day.' Another student says the median is 30 minutes. The class is preparing a display for the school newsletter and wants a measure that represents a typical student without being distorted by the student who read 180 minutes. Ms. Rivera asks them to compute both measures, consider the shape of the data, and decide what to report and how to explain it. The class has calculators and a blank dot plot.
1. Compute the mean and median and explain why they differ so much. Which is more representative of a typical student in this data set?
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The sum is 20 + 25 + 25 + 30 + 30 + 35 + 35 + 40 + 180 = 420. The mean is 420 ÷ 9 ≈ 46.7 minutes. The ordered data have a median of 30 minutes, the fifth value.
The mean is much larger because the 180-minute value is an outlier far above the cluster from 20 to 40. A mean balances the total, so a single very large value pulls it upward. Eight of the nine students read 40 minutes or less, and the median of 30 reflects that typical cluster. For describing a typical student, the median is more representative. The mean is still useful if the question is about total reading divided equally among all students, but it should not be labeled 'typical' without noting the outlier.
2. The student's statement says 'about 47 minutes a day.' Identify the unit and interpretation error and rewrite the statement correctly.
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The 46.7 figure is a weekly total per student, not a daily amount. The student divided the total by the number of students but then mislabeled the result as a daily rate. The data are already weekly totals, so 46.7 means about 47 minutes per student per week.
To express a daily rate, divide by 7: 46.7 ÷ 7 ≈ 6.7 minutes per day. A correct rewrite is: 'On average, a student read about 47 minutes per week, or about 7 minutes per day.' A more typical statement using the median is: 'The typical student read about 30 minutes per week.' The unit label matters because reporting 47 minutes per day would overstate reading by a factor of 7.
3. Design a graph for the newsletter that is honest and clear. Specify axis choices and one label that prevents misreading.
Read the worked answer
Use a dot plot of the nine individual weekly totals, with a horizontal axis labeled 'Weekly reading minutes per student' and a vertical axis showing frequency, or a bar graph with the same horizontal scale. Start the horizontal axis at 0 so the visual distances reflect the actual differences. Mark the median at 30 and optionally the mean at about 47 with separate labels.
A dotted vertical line or annotation should identify the 180-minute value as an outlier. Include the sample size (n = 9) and a caption such as 'Each dot represents one student's total for the week.' Avoid a truncated axis that starts at 20, which would exaggerate the spread. The label prevents the common misreading that the graph shows daily minutes rather than weekly totals.