Statistical Graphs and Frequency Distribution

Types of Statistical Graphs

• Statistical graphs organize and display data visually.
• Different graphs are best for different types of data.
• Graphs help analyze data trends and patterns.

Frequency Distribution Table

• A frequency distribution table organizes data.
• It shows the frequency (or number of occurrences) of a variable.
• The table shows categories, frequency, relative frequency, and percentage.
• The sum of all relative frequencies equals 1.
• The sum of all percentages equals 100.
• The category column lists the items being considered.
• Frequency is the number of times each category appears in the data.
• Relative frequency shows a category's proportion compared to the total data set.

Bar Graph

• Bar graphs compare data categories.
• Categories are represented by bars of different heights/lengths that correspond with the frequencies of those categories.
• Best for nominal and discrete data (nationality, gender).
• Bar graphs are also used to display frequency data, like population sizes or other similar information.

Histograms

• Histograms present frequency distributions graphically.
• Rectangular bars represent data ranges with no space between them.
• Bar height represents the frequency of the range.
• Bar width represents the interval's range.

Frequency Polygon

• A frequency polygon plots frequency against class marks.
• Show changes in data over time, e.g., temperature changes, population, income.
• Connected points represents sequential categories or data.

Ogive Graph

• Ogive plots cumulative frequency against class boundaries.
• The graph is always non-decreasing because cumulative frequencies increase.
• Useful for determining the number of data points below or above a certain value within specified intervals.

Line Graph

• Line graphs display data changes over time.
• Useful for time-series data.
• Plot data points to show trends or patterns.

Pictograph

• Pictographs use pictures/symbols to show numerical data.
• A legend explains the symbol-value relationship, enabling proportions to be easily calculated from the graph.
• Visual representation of data that is easy to understand at a glance.

Stem and Leaf Plot

• A stem-and-leaf plot arranges data values into stems (first digit) and leaves (last digit).
• Organizes data for easy interpretation.

Interpretation of Statistical Graphs

• Interpreting statistical visuals involves recognizing elements like titles, labels, scales, and data points.
• Understanding graph type is essential to understanding it's interpretation.
• Trends and patterns can be visualized.

Components of a Statistical Graph

• Graph title for topic, axis, labels for units, graph data, and graph units are important components.
• Data points represented in the graph.
• Graph units are important for comparison of the measure.
• Graph axis labels correctly identify the values represented along each axis.