2017AP Statistics Summer Packet.pdf

Constructing a boxplot 1 draw a horizontal line and

Info icon This preview shows pages 19–22. Sign up to view the full content.

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.
Image of page 19

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

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
Image of page 20
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.
Image of page 21

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Image of page 22
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern