2017AP Statistics Summer Packet.pdf

# Constructing a boxplot 1 draw a horizontal line and

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or stemplots, they are best used for side-by-side comparison of more than one distribution. Constructing a boxplot: 1. Draw a horizontal line, and label it with the variable being graphed. Scale the axis based on the values of the variable 2. Mark a dot where the maximum and minimum values lie (above the horizontal line). 3. Draw vertical lines where the Q 1 , M , and Q 3 lie. 4. Connect the vertical lines to create a box around them. Draw horizontal lines from the box to connect to the maximum and minimum values. 5. Provide a descriptive title. Practice Problem: 4. Students from a statistics class were asked to record their heights in inches: 65 72 68 64 60 55 73 71 52 63 61 65 74 69 67 74 50 44 75 67 62 66 80 64 Construct a boxplot of the data.

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20 Modified boxplots are boxplots that show the outliers as individual points. To construct a modified boxplot, first calculate if there are any outliers (any observation(s) that is more than 1.5 x IQR outside the median). Plot any outliers as individual points. Now construct a boxplot, but the new maximum and minimum are the smallest and largest observations that are not outliers. Example: Now, complete Worksheet E (Histograms & Boxplots); page 33
21 Part 6: Describing Quantitative Graphs In any graph of data, look for the overall pattern and for any striking deviations from the pattern. You can describe the overall pattern of a distribution by its shape , center , and spread . Shape: The data on the graph may resemble one of the distinct patterns below, or may show no special shape. Symmetric: The left and right sides are approximately mirror images. Skewed Left: There is a “tail” of data that extends far to the left. Skewed Right: There is a “tail” of data that extends far to the right. Uniform: All data values occur at roughly the same frequency (all “bars” are equally high). Unimodal: The graph has one distinct peak. Bimodal: The graph has two distinct peaks. Center: You can estimate the center of a distribution by visually examining the graph, or by calculating one of the common measures of center: Mean: The average of all of the data values. The mean is significantly affected by extreme outliers (it is not “resistant”). Median: The middle value, when the data is ordered from smallest to greatest. When there is an even number of values, the middle two numbers are averaged to determine the median. The median is unaffected by extreme outliers (it is “resistant”). Spread: Below are two sets of data that are both symmetric and have the same mean and median: Set I: 15, 15, 15, 15, 15, 15, 15, 15 Set II: 1, 1, 1, 1, 29, 29, 29, 29 What distinguishes them is how widely spread the data is. There are several measures of spread in describing the distribution of a variable: Range: Max. Value Min Value Inter-Quartile Range: More on this when we discuss boxplots. Variance or Standard Deviation: More on this later. Unusual Features: These include any significant deviations from the overall pattern, including: Outliers: These are individual values that fall outside of the overall pattern.

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