 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum  MENU          Solutions for Session 3, Part A

See solutions for Problems: A1 | A2 | A3 | A4 | A5 | A6| A7| A8| A9    Problem A1 The range of data values is from 33 to 89, which is probably too wide for a line plot to be useful. Furthermore, there is so much variation to the data that a line plot probably would not indicate any clear trends.   Problem A2 The initial construction of the stem and leaf plot looks like this:    Problem A3 The ordered stem and leaf plot looks like this:    Problem A4

 a. All 26 estimates are between 33 and 89 seconds, as the ordered stem and leaf plot indicates. b. Sixteen of the 26 estimates are between 52 and 68 seconds. Nine are between 52 and 59 seconds, and seven are between 60 and 68 seconds.   Problem A5

 a. There are six estimates below 55 seconds and 10 estimates above 65 seconds. In total, 16 of the 26 estimates were more than five seconds away from one minute. b. Since 16 estimates were more than five seconds away from one minute, the remaining 10 of 26 estimates were within five seconds of one minute. c. Three estimates were below 50 seconds, and six were above 70 seconds. In total, nine of 26 estimates were more than 10 seconds away from one minute. d. Since nine estimates were more than 10 seconds away from one minute, the remaining 17 of 26 estimates were within 10 seconds of one minute.   Problem A6

 a. The mean is about 62.35, which is found by adding up all the data values and dividing by 26, the number of values in the set. (1,621 / 26 = 62.35). The mean is fairly close to 60 seconds, although we might predict that most people tend to overestimate when 60 seconds have elapsed, based on these 26 observations. b. As the mean is 62.35, there are eight estimates above 67.35 and 10 estimates below 57.35. In total, 18 of 26 estimates are more than five seconds away from the mean. c. There are five estimates above 72.35 and five estimates below 52.35. In total, 10 of 26 estimates are more than 10 seconds away from the mean. d. There is so much variability that the mode does not carry much information. In reality, it is extremely unlikely for two people to come up with exactly identical times for their estimates, since time is a continuous variable.   Problem A7 Before ordering, the stem and leaf plot based on a grouping by fives looks like this: After ordering, the stem and leaf plot based on a grouping by fives looks like this:    Problem A8

There are many descriptive statements that could provide an answer to this question. Here are some things you may have noted in your descriptions:

 • All estimates are between 33 seconds and 89 seconds. The range is 56 seconds, which indicates a lot of variation in the estimates. • There is a concentration of estimates between 52 seconds and 68 seconds. Sixteen of the 26 estimates (or 16 / 26 = 61.5%) fall within this interval. Note that the range of this interval is only 16 seconds. • Only two different values (57 and 59) occur more than once. There is no one value that occurs most frequently. • The most common response time is in the range of 55 to 59 seconds, a range that contains six (23%) of the 26 estimates. • Poor estimates are more likely to be overestimates than underestimates. Only three estimates were 50 or below, while seven estimates were 70 or higher.   Problem A9

 a. A stem and leaf plot of the salaries of people working at a company or the populations of towns in a state would need wider groupings. b. Stem and leaf plots cannot be used for qualitative data, such as gender or car color. A stem and leaf plot may not be very effective when there are few data points or when the data values are close together.     © Annenberg Foundation 2017. All rights reserved. Legal Policy