Descriptive Statistics: Tabular and Graphical Methods
Descriptive Statistics: Tabular and Graphical Methods
Introduction
Course: ECON 3610-001 Business Statistics I
Instructor: Prof. Dr. Debora Mazetto
Dates: January 20 and 22, 2026
Content Overview
Topics Covered:
Data, variables, and levels of measurement
Graphical and tabular methods to describe qualitative data
Frequency table
Cross tabulation
Bar charts
Pie chart
Graphical and tabular methods to describe quantitative data
Line chart
Scatter plot and relations
Histogram
Data: Concepts
Definition of Data:
Data refers to the facts and figures that are collected and analyzed in research.
Data Set:
A collection of data pertaining to a particular study provides information about individual elements such as people or companies.
Variable:
Any characteristic of an individual element that can change or vary.
Observation:
The value of a particular variable for a given element.
Example: In a data set with 10 people (elements), it contains 10 observations.
Data: Example
Example Data Set:
Name | Year | Major | Height (ft) | Credits (semester)
Allan | Freshman | Finance | 5.18 | 15
Bailey | Sophomore | Marketing | 6.04 | 15
Charlie | Sophomore | Marketing | 5.64 | 12
Daniel | Junior | Finance | 6.33 | 18
Elliot | Senior | Finance | 6.14 | 12
Faith | Junior | Marketing | 5.12 | 12
Gail | Junior | Finance | 6.36 | 15
Harley | Freshman | Economics | 5.91 | 12
Isabelle | Senior | Finance | 5.51 | 15
Jamie | Freshman | Marketing | 5.64 | 12
Data Set Breakdown:
Variables: 5
Elements: 10
Observations: 10
Data Measurement
Measurement Process:
To describe any variable in a data set, a measurement is carried out to assign a value.
Types of Data Measurement:
Qualitative or Categorical:
Values depict groups or categories, can be labels or numbers.
Nominal:
Labels/names denoting attributes (e.g., gender, car color).
Ordinal:
Like nominal but represents order/rank (e.g., college year, teaching rating).
Quantitative:
Values represent quantities and are always numeric.
Interval:
Values expressed as fixed units of measure (e.g., temperature, SAT score).
Ratio:
Same as interval with an absolute zero reflecting the absence of quantity (e.g., profit, earnings).
Data Measurement: Example
Example Data Set:
Name | Year | Major | Height (ft) | Credits (semester)
Allan | Freshman | Finance | 5.18 | 15
Bailey | Sophomore | Marketing | 6.04 | 15
Charlie | Sophomore | Marketing | 5.64 | 12
Daniel | Junior | Finance | 6.33 | 18
Elliot | Senior | Finance | 6.14 | 12
Faith | Junior | Marketing | 5.12 | 12
Gail | Junior | Finance | 6.36 | 15
Harley | Freshman | Economics | 5.91 | 12
Isabelle | Senior | Finance | 5.51 | 15
Jamie | Freshman | Marketing | 5.64 | 12
Categorization of Variables:
Qualitative Variables:
Nominal: Name and Major
Ordinal: Year
Quantitative Variables:
Interval: Height
Ratio: Credits
Data Measurement: Summary
Categories of Variables:
Qualitative/Categorical:
Nominal
Ordinal
Quantitative:
Interval
Ratio
Frequency Distribution: Concepts
Definition:
Frequency distribution summarizes qualitative data by showing how many observations fall into each category.
Terms:
Frequency:
The count of observations in each non-overlapping category (label).
Relative Frequency:
The proportion of observations in each category, calculated as:
Cumulative Frequency:
The sum of the relative frequencies of all previous categories.
Frequency Distribution: Example
Example of Frequency Distribution for Students Per Major:
Major | Frequency | Relative Frequency | Cumulative Frequency |
Finance | 5 | 0.50 | 0.50
Marketing | 4 | 0.40 | 0.90
Economics | 1 | 0.10 | 1.00
Total: 10 | 1.00 | -
Calculations:
Sum of all frequencies equals total number of observations:
Each relative frequency calculated as:
Finance:
Marketing:
Economics:
Cumulative frequency of the last category always equals 1.
Frequency Distribution: Using Excel
Example Template in Excel:
Columns: Name, Year, Major, Height (ft), Credits (semester)
Excel Formulas Used:
To calculate frequency:
ext{COUNTIF}($C$2:$C$11; G2)
Relative Frequency Formula:
Complete Frequencies and Relative Frequencies:
Total number of students: 10
Sum of relative frequency equals 1.
Cross Tabulation: Concepts
Definition:
A cross tabulation displays a tabular summary of two variables, allowing for comparison between categories.
Structure:
Rows categorize by one variable (e.g., major), while columns categorize by a second variable (e.g., year).
Frequency Display:
Can show either frequency or relative frequency of each category combination.
Cross Tabulation: Example
Example Cross Tabulation Displaying Major by Year:
Major | Total | Finance | Marketing | Economics
Freshman | 3 (1, 1, 1)
Sophomore | 2 (0, 2, 0)
Junior | 3 (2, 1, 0)
Senior | 2 (2, 0, 0)
Total: 10 (5, 4, 1)
Cross Tabulation: Relative Frequency Example
Relative Frequencies for Each Category:
Major | Total | Finance | Marketing | Economics
Freshman | 0.30 (0.10, 0.10, 0.10)
Sophomore | 0.20 (0.00, 0.20, 0.00)
Junior | 0.30 (0.20, 0.10, 0.00)
Senior | 0.20 (0.20, 0.00, 0.00)
Total: 1.00
Observations:
20% of students are in Junior year and Finance major.
Bar Chart
Definition:
A bar chart is used for displaying qualitative data by showing the frequency of each category.
Structure:
The horizontal axis contains the category labels, while the vertical axis shows frequency or relative frequency.
Advantages:
Provides quick visibility of which groups have the highest or lowest frequencies, and easy comparison of categories.
Example:
Display categories like Finance, Marketing, and Economics with safe illustrative frequency data.
Stacked Bar Chart
Definition:
A stacked bar chart includes segments of different colors to compare two variables in a single bar chart display.
Usage:
Visualize two data sets simultaneously, effectively demonstrating relative proportions.
Example:
Overall majors by year in segments for Freshman, Sophomore, Junior, and Senior.
Pie Chart
Definition:
A pie chart visually represents the proportion of categories as slices of a circular pie.
Ideal Use:
Display percentages (e.g., showing if a combination of groups exceeds 50%).
Example:
Distribution of students across majors as segments of the pie chart, illustrating relationships visually.
Line Graph
Definition:
A line graph displays quantitative variable changes over time, showing trends in data points connected by lines.
Example:
Showing unemployment rate over several decades using historical data from U.S. Bureau of Labor Statistics.
Scatter Plot
Definition:
Scatter plots examine relationships between two variables, with one variable plotted along the horizontal axis (x-axis) and the other along the vertical axis (y-axis).
Components:
Each point represents an observation, and the pattern of the points reveals the overall relationship between the two variables.
Trendline:
A line of best fit may be added to demonstrate correlation in the data visualization.
Examples:
Revenue against Temperature illustrating ice cream sales can show how one variable influences another.
Histogram
Definition:
A histogram summarizes numerical data distributions by grouping measurements into classes and displaying the data with bars.
Difference from Bar Graph:
Unlike bar graphs for categorical data, histograms are for quantitative data.
Histograms and Distribution Skewness
Shape Interpretation:
Symmetric:
The left and right tails are mirror images; values cluster around the center.
Right Skewed:
Longer tail to the right; most frequent values are on the left.
Left Skewed:
Longer tail to the left; most frequent values are on the right.
Example:
Data representation should visually depict the skewness and distribution shapes clearly, enhancing understanding of data characteristics.
Conclusion
All figures referenced are hypothetical and used solely for demonstration purposes.
Understanding these statistical tools is crucial for analyzing and interpreting data effectively in business contexts.