2017AP Statistics Summer Packet.pdf

In the example above the lowest observed heart rate

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In the example above, the lowest observed heart rate of 61 beats per minute consists of a “stem” of 6 and a “leaf” of 1. 2. Write the stems vertically in increasing order form top to bottom, and draw a vertical line to the right of the stem values. Examine the data and write each leaf to the right of its stem, spacing the leaves equally. It is good practice to order the stem values from smallest to largest as you write them across the graph. 3. Title your graph, and add a key describing what the stems and leaves represent. 4. If the stems have a large number of leaves, it may be helpful to “split” stems (for example, the stems could go in steps of 5 instead of 10, so one stem could include values from 60-64, and another stem could include 65-69). Now, complete Worksheet D (DotPlots & StemPlots); page 32
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17 Histograms allow us to graph larger sets of data by grouping values together: The graph above represents a sample of the heights of 31 (add the frequency of each bar) black cherry trees. Could we re-create the original data from this graph? Yes No What is the height of the shortest measured tree? 6 0 tree h eig h t< 6 5 . What is the height of the tallest measured tree? 8 5 tree h eig h t< 9 0 . The graph includes the following important elements: Descriptive title. Properly scaled, labeled axes. Classes (“bars”) that are of equal width, and whose heights represent the frequency of observations for they values (tree heights) contained in the class. Unlike a bar graph , order of the bars is important. Let’s build the h istogram, assuming the original data was the following (sorted) heights: 60, 62, 62, 65, 67, 68, 70, 70, 71, 72, 73, 73, 73, 74, 75, 75, 75, 75, 76, 76, 77, 77, 79, 79, 82, 82, 82, 83, 84, 86, 88 Step 1: Determine the number of classes ( k ) to be used. There is no firm rule on determining this, which means that two different people could create two valid, different histograms for the same data. As a guideline, count the number of observations, n , and take the square root of n . Round n to the nearest whole number and use that as the number of classes, k . n = 3 1 # of classes: _ _ _ 6 _ _ _ k n (nearest whole number) Step 2: Determine width of each class. Take the range (max min) and divide by the number of classes, k . Round this number up to the next whole number . This is the class width. Class width: (m ax m in ) w k 8 8 6 0 2 8 5 6 6
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18 Step 3: Construct a frequency table listing the data count in each class: Class Count (Range of Values) 60 65 60 height 65 65 70 65 height 70 70 75 75 80 80 85 85 90 85 height 90 Step 4: Draw and label axes, including the lower & upper bounds of each class on the horizontal axis and the frequency (count) of observations for each class on the vertical axis. Draw bars representing the count in each class, with the bars touching (no spaces in between).
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19 Boxplots (Otherwise Known as the Box and Whisker Plot) The five number summary is used to create a boxplot . Because boxplots show less detail than histograms or stemplots, they are best used for side-by-side comparison of more than one distribution.
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