Exercise Answers: Module 30

Standard Deviation

  1. 25.9 points
  2. 24.5 points
  3. 24 points (which occurred eight times)
  4. all three seem to represent the typical number of points scored; the mean is a bit high because there are no extremely low values but there are a few high values that pull the mean upwards.
  5. 17.7 to 34.1 points
  6. 54 of the 80 game results
  7. yes; 54\div80=67.5\%
  8. 9.5 to 42.3 points
  9. 79 of the 80 game results
  10. sort of close but not really; 79\div80=98.75\%
  11. 1.3 to 50.5 points
  12. 79 of the 80 game results, again
  13. yes, this is pretty close; 79\div80=98.75\%
  14. 60.5; 66.5
  15. 57.5; 69.5
  16. 54.5; 72.5
  17. 66.5; 72.5
  18. 63.5; 75.5
  19. 60.5; 78.5
  20. 68\% because 100\%-(16\%+16\%)=68\%
  21. 195 lb because this is halfway between 160 and 230 lb
  22. 35 lb because 195-35 lb and 195+35 lb encompasses 68\% of the data
  23. 125; 265
  24. 8.8; 15.6
  25. You would not have predicted this from the data because it is more than two standard deviations below the mean, so there would be a roughly 2.5\% chance of this happening randomly. In fact, (12.2-7)\div1.7 is slightly larger than 3, so this is more than three standard deviations below the mean, making it even more unlikely. (You might have predicted that the Patriots would get worse when Tom Brady left them for Tampa Bay, but you wouldn’t have predicted only 7 wins based on the previous nineteen years of data.)
  26. 3.4; 10.2
  27. You would not predict this from the data because it is more than two standard deviations above the mean, so there would be a roughly 2.5\% chance of this happening randomly. In fact, (13-6.8)\div1.7\approx3.6, so this is more than three standard deviations above the mean, making it even more unlikely. This increased win total is partly due to external forces (i.e., the Patriots becoming weaker and losing two games to the Bills) but even 11 wins would have been a bold prediction, let alone 13.
  28. 3.9; 14.3
  29. The trouble with making predictions about the Broncos is that their standard deviation is so large. You could choose any number between 4 and 14 wins and be within the 95\% interval. (9.1-5)\div2.6\approx1.6, so this is around 1.6 standard deviations below the mean, which makes it not very unusual. Whereas the Patriots and Bills are more consistent, the Broncos’ win totals fluctuate quite a bit and are therefore more unpredictable.

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Technical Mathematics by Morgan Chase is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.