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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