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Exploring Distribution with Graphs in Data Analysis

Learn the basics of exploratory data analysis, distributions, categorical vs. quantitative variables, constructing bar graphs, stemplots, histograms, and more. Understand vocabulary like modes, ogive, and seasonal variation.

ivy-mooney
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Exploring Distribution with Graphs in Data Analysis

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  1. Lesson 1 - 1 Displaying Distribution with Graphs

  2. Knowledge Objectives • What is meant by exploratory data analysis • What is meant by the distribution of a variable • Differentiate between categorical variables and quantitative variables • What is meant by the mode of a distribution • What is meant by an outlier in a stemplot or histogram

  3. Construction Objectives • Construct bar graphs and pie charts for a set of categorical data • Construct a stemplot for a set of quantitative data • Construct a back-to-back stemplot to compare two related distributions • Construct a stemplot using split stems • Construct a histogram for a set of quantitative data, and discuss how changing the class width can change the impression of the data given by the histogram

  4. Construction Objectives cont • Describe the overall pattern of a distribution by its shape, center, and spread • Recognize and identify symmetric and skewed distributions • Construct and interpret an ogive (relative cumulative frequency graph) from a relative frequency table • Construct a time plot for a set of data collected over time

  5. Vocabulary • Roundoff error – errors associated with decimal inaccuracies • Pie chart – chart that emphasize each category’s relation to the whole • Bargraph – displays the distribution of a categorical variable • Stemplot – includes actual numerical values in a plot that gives a quick picture of the distribution • Back-to-back stemplot – two distributions plotted with a common stem • Splitting stems – divides step into 0-4 and 5-9 • Trimming – removes the last digit or digits before making a stemplot • Histogram – breaks range of values into classes and displays their frequencies • Frequency – counts of data in a class • Frequency table – table of frequencies

  6. Vocabulary • Modes – major peaks in a distribution • Unimodal – a distribution whose shape with a single peak (mode) • Bimodal – a distribution whose shape has two peaks (modes) • Symmetric – if values smaller and larger of the center are mirror images of each other • Skewed – if smaller or larger values from the center form a tail • Ogive – relative cumulative frequency graph • Time plot – plots a variable against time on the horizontal scale of the plot • Seasonal variation – a regular rise and fall in a time plot

  7. Categorical Data • Categorical Variable: • Values are labels or categories • Distributions list the categories and either the count or percent of individuals in each • Displays: BarGraphs and PieCharts

  8. Categorical Data Example Physical Therapist’s Rehabilitation Sample

  9. Categorical Data • Items are placed into one of several groups or categories (to be counted) • Typical graphs of categorical data: • Pie Charts; emphasizes each category’s relation to the whole • Bar Charts; emphasizes each category’s relation with other categories Bar Chart Pie Chart

  10. Charts for Both Data Types Relative Frequency Chart Pareto Chart Cumulative Frequency Chart

  11. Example 1 Construct a pie chart and a bar graph. Radio Station Formats Why not 100%?

  12. Example 1 Pie Chart

  13. Example 1 Bar Graph

  14. Quantitative Data • Quantitative Variable: • Values are numeric - arithmetic computation makes sense (average, etc.) • Distributions list the values and number of times the variable takes on that value • Displays: • Dotplots • Stemplots • Histograms • Boxplots

  15. Dot Plot • Small datasets with a small range (max-min) can be easily displayed using a dotplot • Draw and label a number line from min to max • Place one dot per observation above its value • Stack multiple observations evenly • First type of graph under STATPLOT 34 values ranging from 0 to 8

  16. Stem Plots • A stemplot gives a quick picture of the shape of a distribution while including the numerical values • Separate each observation into a stem and a leafeg. 14g -> 1|4 256 -> 25|6 32.9oz -> 32|9 • Write stems in a vertical column and draw a vertical line to the right of the column • Write each leaf to the right of its stem • Note: • Stemplots do not work well for large data sets • Not available on calculator

  17. Stem & Leaf Plots Review Given the following values, draw a stem and leaf plot 20, 32, 45, 44, 26, 37, 51, 29, 34, 32, 25, 41, 56 Ages Occurrences ------------------------------------------------------------------ 2 | 0, 6, 9, 5 | 3 | 2, 3, 4, 2 | 4 | 5, 4, 1 | 5 | 1, 6

  18. Splitting Stems • Double the number of stems, writing 0-4 after the first and 5-9 after second.

  19. Back-to-Back Stemplots • Back-to-Back Stemplots: Compare datasets Example1.4, pages 42-43 Literacy Rates in Islamic Nations

  20. Example 1 The ages (measured by last birthday) of the employees of Dewey, Cheatum and Howe are listed below. • Construct a stem graph of the ages • Construct a back-to-back comparing the offices • Construct a histogram of the ages Office A Office B

  21. Example 1a: Stem and Leaf Ages of Personnel 2 0, 1, 2, 6, 8, 8, 3 0, 1, 1, 2, 3, 5, 6, 7, 8, 9, 9, 4 2, 2, 5, 7, 8, 9, 9,

  22. Example 1b: Back-to-Back Stem Office A: Ages of Personnel Office B: Ages of Personnel 20, 8 3 2, 3, 5, 6, 7, 8, 45, 7, 8, 9, 1, 2, 6, 8 0, 1, 1, 9, 9 2, 2, 9

  23. Example 2 Below are times obtained from a mail-order company's shipping records concerning time from receipt of order to delivery (in days) for items from their catalogue? • Construct a stem plot of the delivery times • Construct a split stem plot of the delivery times • Construct a histogram of the delivery times

  24. Example 2: Stem and Leaf Part Days to Deliver 0 2, 3, 3, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9 1 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 9 2 1, 2, 2, 3, 5, 7 3 1

  25. Example 2b: Split Stem and Leaf Days to Deliver 0 2, 3, 3, 4 0 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9 1 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4 1 9 2 1, 2, 2, 3 2 5, 7 3 1

  26. Day 1 Summary and Homework • Summary • Categorical data • Data where adding/subtracting makes no sense • Pie charts and bar graphs • Quantitative data • Data where arithmetic operations make sense • Stem plots and histograms • Some graphs can work for both types of data • Frequency and dot plots • Ogive and Pareto • Homework • pg 46 – 48 problems 1-5

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