1. Chapter 2 Graphical Distributions Distribution – a graphical display of data. After a survey or experiment is complete, different graphing methods are used to display the data.

2. Graphical Data Dotplot – simplest display of quantitative data –Place number of dots over numerical value depending on the frequency of occurrence. –Number is the explanatory data (x-axis), frequency is the response data (y-axis) –(Example: No. of siblings)

3. Histogram Histogram – quantitative data uses frequency table 1.Find class width of “bins”. Class width = max value – min value Number of classes ex: data ranges from 0 to 68, and you want 5 classes class width = 68-0 = 13.6 round up to 14 (always 5round up) 2.Create a table with1) class limits 2) Frequency 3) Midpoint 4) Relative frequency

4. Histogram Histogram table (data p35 table 2-1) Class Midpoint Tally Frequency Relative (=freq/tot no) widths frequency 1-9 9-17 17-25 25-33 33-41 41-49 Left part included, right part is not, for ex. 17 in table bin 17-25.

5. Histogram Histogram Rules –Draw bars connected –x-axis includes class widths –Y-axis includes frequencies and relative frequencies –For data Left part included, right part is not

6. Draw Histogram

7. Shapes of distribution a)Symmetric: unimodal (one high point) mirror image from middle of distribution b)Uniform: every class has equal frequency (toss of die) c)Skewed left: Skewed right direction is toward long tail d)Bimodal – usually indicates different populations or sets of males and females.

8. 2.2 Bar graph, Circular Graphs (pie charts), time series graphs Used for catagorical data (not quantitative)

9. Bar Graph Rules for Bar Graphs –Bars can be horizontal or vertical –Bars are of uniform width and uniformly spaced and do not touch (except when comparing 2 populations) –Lengths of bars represent values being displayed (frequency or percentage of occurrence) –Label graphs clearly,y-axis should be scaled appropriately –If changing scale us squiggle (not always recommended as it can distort meaning of graph)

10. Bar Graph example Number of accidents Ages 16-2526-4546-65+65 # of people 50 345 325 110 # of accidents 22 42 35 33 % accident/people (Create bar graph) Pareto Chart: bar graph arranged with highest to lowest frequency arranged from left to right

11. Circle Graph (Pie Chart) Wedges of circle represent proportion (or percentage) of total population that share a common characteristic. –Can only look at one characteristics –Too many segments can make the graph unclear

12. Time Series Graph Time series graph –Data are plotted in order of occurrence at regular intervals over a period of time –Time is x-axis; variable of interest on y-axis Feb-07 Apr-07 Jun-07 Aug-07 Oct-07 Dec-07 2.42.852.98 2.78 2.78 2.98 Feb-08Apr-08 Jun-08 Aug-08 Oct-08 Dec-08 2.953.44.083.69 3.05 1.6 Feb-09Apr-09Jun-09Aug-09 1.92.052.72.5

13. Which type to use Bar graphs – quantitative or qualitative(with frequency or percentage). Squiggle can be used, but don’t let it misrepresent the data. Pareto charts – bar charts with decreasing order of occurrence. Circle Graph – can display only 1 variable. Most effective with 10 or fewer wedges. Time-series- display how data changes over time

14. Stem-and-Leaf Displays A stem-and-leaf display is a method used to rank order and arrange data into groups Quantitative data Align the stem in a vertical column from smallest to largest. Draw a vertical line. Place all the leaves with the same stem in the same row as the stem with leaves in increasing order. Label display.

15. Stem-and-Leaf Displays Benefits – all individual data points can be identified Split stem can compare two sets of data. For example men and women heights.