1. Lesson 1 – 1a from http://www.pendragoncove.info/statistics/ch1.htm 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 Body PartFrequencyRelative Frequency Back120.4 Wrist20.0667 Elbow10.0333 Hip20.0667 Shoulder40.1333 Knee50.1667 Hand20.0667 Groin10.0333 Neck10.0333 Total301.0000 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 Pie Chart Bar Chart

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

11. Example 1 Construct a pie chart and a bar graph. Radio Station Formats FormatNr of StationsPercentage Adult contemporary1,55611.2 Adult standards1.1968.6 Contemporary Hits5694.1 Country2,06614.9 News/Talk/Info2,17915.7 Oldies1,0607.7 Religious2,01414.6 Rock8696.3 Spanish Language7505.4 Other formats1,57911.4 Total13,83899.9 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 leaf eg. 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. a)Construct a stem graph of the ages b)Construct a back-to-back comparing the offices c)Construct a histogram of the ages 223121492642 30283139 203732363533 454749382848 Office A Office B

21. Example 1a: Stem and Leaf 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, 223121492642 30283139 203732363533 454749382848 Ages of Personnel

22. Example 1b: Back-to-Back Stem 2 0, 8 3 2, 3, 5, 6, 7, 8, 4 5, 7, 8, 9, 223121492642 30283139 203732363533 454749382848 Office B: Ages of PersonnelOffice A: Ages of Personnel 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? a)Construct a stem plot of the delivery times b)Construct a split stem plot of the delivery times c)Construct a histogram of the delivery times 371051412 629222511 5712102223 14854713 2731132168 3101912118

24. Example 2: Stem and Leaf Part 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 Days to Deliver 371051412 629222511 5712102223 14854713 2731132168 3101912118

25. Example 2b: Split Stem and Leaf 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 Days to Deliver 371051412 629222511 5712102223 14854713 2731132168 3101912118

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