Math 4030-1a Descriptive Statistics Tables and Charts 6/9/2018 Math 4030-1a Descriptive Statistics Tables and Charts Descriptive Measures

Organization and description of single variable data from one sample: Tables: (Ungrouped) frequency tables Grouped frequency tables Charts/diagrams: Dot diagram Stem-and-leaf display Bar Chart Pie Chart Pareto diagram Histogram Ogive

Example 1: Categorical, qualitative, nominal level 6/9/2018 Example 1: Categorical, qualitative, nominal level BENG.CIVI.POST BENGDIP.CHEM BENG.MECH.POST BENGDIP.MECH BENGDIP.CIVI BENG.ELEC.POST BENGDIP.MECH.CP BENG.SOFT.POST BSC.UNDE BSC.GENE BENGDIP.ELEC BENG.CHEM.POST BENGDIP.SOFT BENGDIP.CHEM.CP SS.SWB.ENG BENGDIP.ELEC.CP

(Ungrouped) frequency tables: 6/9/2018 (Ungrouped) frequency tables: Classes/Program Frequency/Count) BENG.CIVI.POST 74 BENG.ELEC.POST 45 BENG.CHEM.POST 5 BENG.MECH.POST 7 BENG.SOFT.POST 3 BENGDIP.CIVI 21 BENGDIP.ELEC BENGDIP.ELEC.CP 1 BENGDIP.CHEM 8 BENGDIP.CHEM.CP BENGDIP.MECH 12 BENGDIP.MECH.CP 2 BENGDIP.SOFT 4 SS.SWB.ENG BSC.UNDE BSC.GENE Total 189 Classes/Program Frequency/Count) CIVI 95 ELEC 49 CHEM 14 MECH 21 SOFT 7 Others 3 Total 189

Include relative frequencies: 6/9/2018 Classes/Program Frequency/Count) Relative Frequency (%) BENG.CIVI.POST 74 39.15% BENG.ELEC.POST 45 23.81% BENG.CHEM.POST 5 2.65% BENG.MECH.POST 7 3.70% BENG.SOFT.POST 3 1.59% BENGDIP.CIVI 21 11.11% BENGDIP.ELEC BENGDIP.ELEC.CP 1 0.53% BENGDIP.CHEM 8 4.23% BENGDIP.CHEM.CP BENGDIP.MECH 12 6.35% BENGDIP.MECH.CP 2 1.06% BENGDIP.SOFT 4 2.12% SS.SWB.ENG BSC.UNDE BSC.GENE Total 189 100.00% Include relative frequencies: Classes/Program Frequency/Count) Relative Frequency (%) CIVI 95 50.26% ELEC 49 25.93% CHEM 14 7.41% MECH 21 11.11% SOFT 7 3.70% Others 3 1.59% Total 189 100.00%

6/9/2018 Bar Chart: Pareto Chart:

Example 2. Qualitative, categorical, ordinal level 6/9/2018 Example 2. Qualitative, categorical, ordinal level Ungrouped Frequency Table Classes Grade Relative F Cumulative AA 3 0.02 A 19 0.14 0.16 B 43 0.31 0.46 C 51 0.36 0.83 D 17 0.12 0.95 F 7 0.05 1.00 Total 140   B C AA A F D

Not recommended for ordinal variables: Pie chart Pareto chart 6/9/2018 Ogive Not recommended for ordinal variables: Pie chart Pareto chart

Example 3. Quantitative, numerical, discrete (not very many values) 6/9/2018 Example 3. Quantitative, numerical, discrete (not very many values) Number of Accidents at Intersections # of Accidents Frequency/Counts 15 1 12 2 10 3 8 4 9 5 6 7 Total 60 2 7 1 4 3 6

Example 4. Quantitative, numerical, continuous, with many values 6/9/2018 Example 4. Quantitative, numerical, continuous, with many values 71 72 74 67 97 68 76 78 65 70 80 29 83 82 66 52 55 81 50 75 64 51 54 63 56 77 60 53 84 62 69 58 95 25 61 34 45 85 90 57 73 21 Groups Count Cumulative 0 - 40 6 41 - 50 3 9 51 - 60 30 39 61 - 70 44 83 71 - 80 43 126 81 - 90 12 138 91 - 100 2 140 Total   Group setting: Include all possible values; No overlapping Number of classes Equal width Class limits choice

Example 4. Quantitative, numerical, continuous, with many values 6/9/2018 Example 4. Quantitative, numerical, continuous, with many values “Bar chart”  histogram Number of classes effect the shape of histogram Density Histogram  Probability density function Cumulative densith histogram  Ogive  cumulative distribution function

ungrouped frequency table, bar chart (or Pareto chart, Pie chart); 6/9/2018 Nominal: ungrouped frequency table, bar chart (or Pareto chart, Pie chart); Ordinal: ungrouped frequency table, bar chart; Scale (few values or discrete): Scale (many values or continuous, small data set): dot diagram, stem-and-leaf display; Scale (many values or continuous, large data set): grouped frequency table, histogram.

6/9/2018 Mean and Median: For a finite collection of (numerical) values (from a sample): The (sample) mean is defined as After reorder the values from the smallest to the largest, i.e. The (sample) median is defined as

Mean vs. Median Mean : a balance point Median : 50-50 dividing point June 9, 2018 Mean vs. Median Mean : a balance point Median : 50-50 dividing point Which one can be more affected by outliers? Requirement of variable/data type? When the data distribution is skewed.

Population Variance and Standard Deviation June 9, 2018 Population Variance and Standard Deviation Equivalent formula:

Sample Variance and Standard Deviation June 9, 2018 Sample Variance and Standard Deviation Equivalent formula:

Coefficient of Variation June 9, 2018 Coefficient of Variation Measures relative variation Always in percentage (%) Is used to compare two or more sets of data measured in different units Requirement of the variable/data type.