Warm up: At what number do you think this ruler would balance on a pencil point?
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- Florence Barnett
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1 Warm up: At what number do you think this ruler would balance on a pencil point? By making a visual estimate we can see the balance point would be at 6. A balance point is a position that balances the sum of the distances to the right of the balance point with the sum of the distances to the left of the balance point.
2 Date: Consider the follow example of quarters taped to lightweight ruler 1. Sam taped 3 quarters to his ruler. The quarters were taped to the posions 1 inch, 9 inches, and 11 inches. If the pencil was placed under the posion 5 inches, do you think the ruler would balance? Why or why not?
3 2.If the ruler did not balance, would you move the pencil to the le or to the right of 5 inches to balance the ruler? Explain your answer. Assuming your balance point is 6 Position of quarter 1 Distance from quarter to your estimate of the balance point What is the sum of the distances to the right of your esmate of the balance point? 4. What is the sum of the distances to the le of your esmate of the balance point?
4 Do you need to adjust the posion of your balance point? If yes, explain how? 6. Calculate the mean and the median of the posion of the quarters. Does the mean or the median of the posions provide a beer esmate of the balance point for the posion of the 3 quarters taped to this ruler? Explain why you made this selecon. Twenty two students from the junior class and twenty six students from the senior class at River City High School parcipated in a walkathon to raise money for the school s band. Dot plots indicang the distances in miles students from each class walked are shown below: 7. Esmate the mean number of miles walked by a junior and mark it an X on the junior class dot plot. How did you esmate this posion? 8. What is the median of the junior data distribuon?
5 9. Is the mean number of miles walked by a junior less than, approximately equal to, or greater than the median number of miles? If they are different, explain why? If they are approximately the same, explain why? 10. How would you describe the typical number of miles walked by a junior in this walkathon? 11. How would you describe the typical number of miles walked by a junior in this walkathon? 11. Esmate the mean number of miles walked by a senior and mark it with an X on the senior class dot plot. How did you esmate this posion? 12. What is the median of the senior data distribuon?
6 13. Esmate the mean and the median of the miles walked by the seniors. Is your esmate of the mean number of miles less than, approximately equal to, or greater than the median number of miles walked by a senior? If they are different, explain why? If they are approximately the same, explain why? 14. How would you describe the typical number of miles walked by a senior in this walkathon? 15. A junior from River City High School indicated that the number of miles walked by a typical junior was beer than the number of miles walked by a typical senior. Do you agree? Explain your answer.
7 Finally, the twenty five sophomores who parcipated in the walkathon reported their results. A dot plot is shown 16. What is different about the sophomore data distribuon compared to the data distribuons for juniors and for seniors? 17. Esmate the balance point of the sophomore data distribuon. 18. What is the median number of miles walked by a sophomore? 19. How would you describe the sophomore data distribuon?
8 Lesson Summary: The mean of a data distribuon represents a balance point for the distribuon. The sum of the distances to the right of the mean is equal to the sum of the distances to the le of the mean.
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