Algebra 1 Summer Institute 2014

The Minute Paradigm

How good is their sense of time?

Without a timing device, how well can you judge the actual length of a minute?

Are some people better at judging elapsed time than others?

  1. In groups of two, one partner will time the other judge the actual length of a minute. The person using a timer will round the time to the nearest second. Partners switch roles. What were your times?

Partner 1 Time / Partner 2 Time
  1. a. How could the data from the whole class be organized?

b. Would a line plot be useful in this case? Why or why not?

  1. Create a Stem and Leaf Plot
  1. How well do people judge when a minute has elapsed?

Based on the ordered plot: (numbers can be changed)

  1. How many of the estimates are between 33 and 89 seconds (inclusive)?
  1. How many of the estimates are between 52 and 68 seconds (inclusive)?

Since the goal is to estimate when a minute has elapsed, it makes sense to consider how close the estimates are to the correct response, which is 60 seconds.

  1. How many people's estimates were more than five seconds away from one minute? That is, how many of the responses were less than 55 seconds or greater than 65 seconds?
  1. How many estimates were within five seconds of one minute?
  1. How many estimates were more than 10 seconds away from one minute?
  1. How many estimates were within 10 seconds of one minute?
  1. Determine the mean of the data set
  2. How does the mean compare to the correct response of 60 seconds?
  1. How many people's estimates were more than 5 seconds away from the mean?
  1. How many people's estimates were more than 10 seconds away from the mean?
  1. Why is it not useful to calculate the mode for this data set?
  1. A stem and leaf plot, however, does not have to group the data by tens -- we could have grouped by fives, for instance. If we were grouping by fives, we would consider all possible numbers in the 50s, for instance, and then put them in two groups, the High and the Low:

Low Group / High Group
50 51 52 53 54 / 55 56 57 58 59

Create a stem and leaf plot grouped by fives:

Based on the stem and leaf plot grouped by fives, give two descriptive statements that provide an answer to the question "How well do people judge when a minute has elapsed?" Answers should take into account the variation in the data.

  1. Think of a situation in which it would be useful to create a stem and leaf plot that would be grouped by a number larger than 10.

When would a stem and leaf plot be impractical or would not be an effective way to present your data?

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