Paper airplanes
Once again I had the MS 150 Statistics students throw paper aircraft from the second floor balcony to obtain statistics. The data generated from both this term and two earlier terms is available in a Google Docs spreadsheet.
A head wind held down the distances this term and kept outliers from occurring. Some planes were lofted up onto the roof, providing a ready made example of the inability to measure a population. In the course of three sections, four planes were lofted onto the roof.
The leftmost three boxplots were from this term, se1, 8:00, 9:00 and 10:00 o'clock sections.
Planes that went back onto the first floor porch were measured as negative distances. Distances were measured not along the flight path but rather perpendicular to the building. Distance out from the building is used. Measuring flight path distances would take longer and circular spirals would be particularly problematic. Measuring perpendicular distances can done in ten minutes or less. An 800 centimeter tape rule is in use in the above image.
This term I opted to do paper aircraft on Monday, with plans to do FiboBelly on Wednesday. Friday is faculty development day, FiboBelly will make a better work sheet for the long weekend as the work sheet already includes the introduction to a confidence interval using z-scores. The issue of small n and the student's t-distribution will be next week.
There was a reason for advancing the exercise by one day: the paper aircraft are fairly reliable at producing a right skewed data distribution. Short flights are more common than long flights. The data is skewed, but the distribution of the sample means should still be roughly normal provided I have more than 30 sample means, which I did not. I suspect that normality would also be more assured if each sample was at least thirty aircraft distances, but few sections have 30 students at this point in the term.
The distribution of the means is not actually as normal as the line chart makes them appear, but the educational intent is to provide a visual that reinforces the statistical concepts of the standard error of the mean being less than the standard deviation of the data. The distribution of the means is narrower with higher relative frequencies. Another seven terms of three sections and I might have the thirty means.
A head wind held down the distances this term and kept outliers from occurring. Some planes were lofted up onto the roof, providing a ready made example of the inability to measure a population. In the course of three sections, four planes were lofted onto the roof.
Boxplot produced using Gnumeric
The leftmost three boxplots were from this term, se1, 8:00, 9:00 and 10:00 o'clock sections.
Planes that went back onto the first floor porch were measured as negative distances. Distances were measured not along the flight path but rather perpendicular to the building. Distance out from the building is used. Measuring flight path distances would take longer and circular spirals would be particularly problematic. Measuring perpendicular distances can done in ten minutes or less. An 800 centimeter tape rule is in use in the above image.
This term I opted to do paper aircraft on Monday, with plans to do FiboBelly on Wednesday. Friday is faculty development day, FiboBelly will make a better work sheet for the long weekend as the work sheet already includes the introduction to a confidence interval using z-scores. The issue of small n and the student's t-distribution will be next week.
Dana recording data, photos by a student
There was a reason for advancing the exercise by one day: the paper aircraft are fairly reliable at producing a right skewed data distribution. Short flights are more common than long flights. The data is skewed, but the distribution of the sample means should still be roughly normal provided I have more than 30 sample means, which I did not. I suspect that normality would also be more assured if each sample was at least thirty aircraft distances, but few sections have 30 students at this point in the term.
Relative frequency line chart histogram produced using Gnumeric
The distribution of the means is not actually as normal as the line chart makes them appear, but the educational intent is to provide a visual that reinforces the statistical concepts of the standard error of the mean being less than the standard deviation of the data. The distribution of the means is narrower with higher relative frequencies. Another seven terms of three sections and I might have the thirty means.
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