Unit 2 – Graphical Representation The Minute Paradigm Unit 2 – Graphical Representation 5/3/2019 Algebra 1 Institute
How long is a minute? How good is your 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? 5/3/2019 Algebra 1 Institute
Groups of Two Take turns One person estimates the length of a minute The other person times, with a timer, the first one. Times are rounded to the nearest second 5/3/2019 Algebra 1 Institute
Organizing Data Dot Plot? Why or why not? 5/3/2019 Algebra 1 Institute
Stem and Leaf Plot Each stem of a stem and leaf plot is determined from the leftmost digit(s) of each number 5/3/2019 Algebra 1 Institute
How Well Do People Judge When a Minute Has Elapsed? How many of the estimates are between 33 and 89 seconds (inclusive)? How many of the estimates are between 52 and 68 seconds (inclusive)? 5/3/2019 Algebra 1 Institute
How Close are the Estimates to 60 seconds? 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? How many estimates were within five seconds of one minute? How many estimates were more than 10 seconds away from one minute? How many estimates were within 10 seconds of one minute? 5/3/2019 Algebra 1 Institute
Mean of Data How does the mean compare to the correct response of 60 seconds? How many people's estimates were more than 5 seconds away from the mean? How many people's estimates were more than 10 seconds away from the average? Why is it not useful to calculate the mode for this data set? 5/3/2019 Algebra 1 Institute
Less Typical Stem and Leaf Plots Create a stem and leaf plot for the following data: 2.3, 3.5, 3.1, 2.9, 2.2, 1.9, 1.3, 3.5, 1.1, 2.0 5/3/2019 Algebra 1 Institute
Less Typical Stem and Leaf Plots 5/3/2019 Algebra 1 Institute
5/3/2019 Algebra 1 Institute
5/3/2019 Algebra 1 Institute
Different Situations When would a stem and leaf plot be impractical or would not be an effective way to present your data? 5/3/2019 Algebra 1 Institute
From a stem plot to a Histogram 5/3/2019 Algebra 1 Institute
Histogram For larger data sets, the stem and leaf plot is not a practical way to organize data It describes ranges of data values rather than specific data values 5/3/2019 Algebra 1 Institute
Advantages/Disadvantages? A histogram offers a better graphical perspective on an entire large data set. One disadvantage is that the actual data values cannot be determined from a histogram, only the number of values within intervals. 5/3/2019 Algebra 1 Institute
5/3/2019 Algebra 1 Institute
Using Histogram According to the histogram and grouped frequency table, how many people's estimates were outside the interval from 50 to less than 70 seconds? That is, how many estimates were less than 50 seconds or 70 seconds or more? How many estimates were within the interval from 50 to less than 70 seconds? If people's estimates were more than 10 seconds away from one minute, does that imply that the people in this group were not as good at estimating a minute's time? 5/3/2019 Algebra 1 Institute
Relative Frequency Histogram 5/3/2019 Algebra 1 Institute
Relative Frequency Histogram What percentage of the responses are in the 70s and below? What percentage of the responses are 80 or higher? What percentage of the responses are 60 or higher? What percentage of the responses are at least 40 but below 70? What percentage of the responses are 65 or greater? What percentage of the responses are equal to 60? 5/3/2019 Algebra 1 Institute
Graphs in GeoGebra Enter all data points in Column A of the spreadsheet Select all data points by clicking on the first cell (A1), holding the shift key in the keyboard, and then click on the last cell (A40). Click on the “One Variable Analysis” Tool A new window pops up. Click on the “Analyze” button. Different charts can be chosen, participants can change from histogram, to bar chart, to dot plot, to stem and leaf plot. In Unit 3 we will work with boxplots in depth. 5/3/2019 Algebra 1 Institute
Graphs in Excel The data points can be copied and pasted from GeoGebra to Excel. Copy them starting on cell A2. Use cell A1 for a title, for example: estimates or length of min. Participants can choose from column, line, pie, bar, scatter. Notice that these representations create one column or bar for each data points. Data is not grouped 5/3/2019 Algebra 1 Institute
Histogram in Excel To group data, define the intervals on column C. In this example, we have been working with intervals of 10. We could have the following intervals: 30-39, 40-49, 50-59, 60-69, 70-79, 80-89. Next, we need to set the frequency. How many data points are in each interval? Enter the frequency manually. Once the intervals and frequencies are set, select those cells (not including the titles), click on charts and select “Column”. To format the graph, click on “Chart Layout”, add the chart title and the axis title. To eliminate the gaps in between columns, right click on one of the columns, select “Format Data Series”. On the tab “Options” change the gap width to 0%. 5/3/2019 Algebra 1 Institute