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

2. 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

3. 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

4. (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

5. 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. 6/9/2018
Bar Chart:
Pareto Chart:

7. Example 2. Qualitative, categorical, ordinal level
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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

8. Not recommended for ordinal variables: Pie chart Pareto chart
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Ogive
Not recommended for ordinal variables:
Pie chart
Pareto chart

9. Example 3. Quantitative, numerical, discrete (not very many values)
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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

10. Example 4. Quantitative, numerical, continuous, with many values
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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 3 9 30 39 44 83 43
126 12
138 2
140
Total
Group setting:
Include all possible values;
No overlapping
Number of classes
Equal width
Class limits choice

11. Example 4. Quantitative, numerical, continuous, with many values
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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

12. ungrouped frequency table, bar chart (or Pareto chart, Pie chart);
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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.

13. 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

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

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

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

17. 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.