Graphing Data

Graphing DataFrequency Distributions

Graphing DataFrequency DistributionsEach value of interest listed on the x-axisBest suited when variable has small, finite number of possible values

What types of variables fit this definition?

Graphing DataStem-and-Leaf Displays

Graphing DataStem and leaf displaysStem = Leading Digit = Most Significant DigitLeaf = Trailing Digit = Least Significant DigitUnlike frequency distribution, can reconstruct entire raw data set very easilyStem is typically tens digit (Xx), but can be hundreds (Xxx) if all values are 100+ or the thousands (Xxxx) if all values are 1,000+Bad if we have many of our values under one stem

Graphing DataStem-and-Leaf Displays

Graphing DataStem-and-Leaf DisplaysBDI2TOT Stem-and-Leaf Plot Frequency Stem & Leaf28.00 0 * 000000000000000011111111111125.00 0 t 222222222222333333333333323.00 0 f 4444444444445555555555530.00 0 s 66666666666666666677777777777722.00 0 . 888888888889999999999917.00 1 * 0000000111111111118.00 1 t 22222222222333333314.00 1 f 444444445555559.00 1 s 66666777718.00 1 . 8888888899999999996.00 2 * 0001112.00 2 t 336.00 2 f 4455554.00 2 s 66772.00 2 . 881.00 3 * 12.00 3 t 2211.00 Extremes (>=35)Stem width: 10Each leaf: 1 case

Graphing DataPut the following data in a stem and leaf plot using the *, t, f, s, . system

Graphing DataHistogramsBars represent certain interval in this case 10 units1st bar = 0-10, 2nd bar = 11-20, etc.Best for data that fall into intervals naturally, i.e. discrete, categorical, nominal or sometimes ordinal variables

Graphing DataHistogramsWhen choosing graph intervals, only rule is to maximize quick readabilityOutlier

Graphing DataHistograms2nd bar = 11-20In practice though, a score of 10.5 would be rounded to 11, and a score of 20.4 to 20, and so our actual range is from 10.5 20.4these are called the real upper limits and the real lower limits11-20 = upper and lower limits 10.5-20.4 = real upper and lower limits

What are the real limits for our 3rd bar (21-30)?

Graphing DataLine GraphsBest for when data continuous, dimensional, or on interval or ratio scalesSame as previous histogram, but provides much richer information if this information is meaningful, use a line graph if its just noise, use a bar graph

Graphing Data

Graphing Data

Chart1

51211

71513

101725

6415

3311

227

Sheet1

5710632

121517432

11132515117

Sheet1

Sheet2

Sheet3

Graphing DataWays to Describe a Graph:Symmetry

Modality

Skewness

Kurtosis

Graphing DataWays to Described a Graph:Symmetry (the graph below is Symmetric)

Graphing DataWays to Described a Graph:Modality (the graph below is Bimodal)

Graphing DataWays to Described a Graph:Skewness (the graph below is Right/Positively Skewed, and hence Non-symmetric)

Graphing DataWays to Described a Graph:Kurtosis

Graphing DataWays to Described a Graph:Kurtosis

Graphing DataWays to Described a Graph:Kurtosis