frequency tables

Frequency as a Statistical Measurement

• Definition: Frequency is a statistical measurement used to track the number of occurrences within a given time period.

• Purpose: It helps to summarize and interpret data in various contexts.

Types of Frequency Measurements

• Types: There are multiple types of frequency measurements, critical to distinguish based on real-life applications.

• Usage: Different frequency measurements are used for summarizing and visualizing data effectively.

Objectives of the Lesson

• At the end of the lesson, students will be able to:

  • Identify definitions of parts of a frequency table or histogram and their uses.

  • Interpret frequency data, tables, and histograms to solve mathematical problems.

Frequency Table

• Definition: A frequency table is a table that lists data values and uses tally marks, numbers, and/or percentages to show the number of times that value appears in the dataset.

  • Purpose: To summarize the frequency of values found in a dataset.

• Essential Components:

  • Frequency Distribution: The group of values or intervals used to separate observations in the dataset.

  • Absolute Frequency: The actual number or tally marks representing how many times a value appears in the dataset.

  • Relative Frequency: A percentage equal to the absolute frequency of a value divided by the total number of data observations in the set.

  • Formula: $ext{Relative Frequency} = rac{ ext{Absolute Frequency}}{ ext{Total Observations}} imes 100$

  • Cumulative Frequency: A percentage that equals the relative frequency of a value added to the relative frequency of all preceding data values in the frequency distribution.

  • Calculation method: Add relative frequencies for all preceding values to find cumulative frequency.

• Structure: A frequency table must include at least two columns but can have up to four columns, varying the number of rows depending on the number of values in the frequency distribution.

Example: NFL Offensive Teams' Points

• Context: A frequency table displaying the average points scored per game for NFL offensive teams during the 2009 regular season.

  • Columns:

  • Left Column: Frequency distribution, showing average points rounded to the nearest point.

  • Right Column: Absolute frequency, where each tally mark corresponds to one NFL team.

• Relative Frequency Calculation:

  • Example: To find the relative frequency of an average of 18 points:

  • Formula application: rac{3}{32} imes 100 = 9.4 ext{%}

  • Interpretation: 9.4% of NFL teams scored an average of 18 points per game during the 2009 season.

• Cumulative Frequency Calculation:

  • To find the cumulative frequency for the point value 15:

  • Calculation: 3.1 ext{%} + 3.1 ext{%} + 6.3 ext{%} = 12.5 ext{%}

  • Interpretation: This means that 12.5% of NFL teams scored an average of 15 points or less per game during that season.

Example: Airline Ticket Prices at US Airports

• Context: A frequency table displaying the average cost of airline tickets from the 100 most traveled US airports in 2009.

  • Columns:

  • Left Column: Frequency distribution, with intervals showing average ticket prices rounded to the nearest dollar.

  • Right Column: Absolute frequency of each interval.

• Question Analysis:

  • About $350 Average Price: Determine how many airports had an average ticket price higher than $350 by summing the relevant intervals.

  • Calculation: $20 + 6 + 1 = 27$

  • Conclusion: 27 airports had an average ticket price higher than $350.

• Relative Frequency Calculation:

  • Ticket Prices Between $300 and $349:

  • Absolute frequency from the table: 34.

  • Calculate relative frequency: rac{34}{100} imes 100 = 34 ext{%}

• Cumulative Frequency Calculation:

  • For ticket prices between $250 and $299:

  • Cumulative frequency based on previous intervals: 1 ext{%} + 7 ext{%} + 31 ext{%} = 39 ext{%}

  • Interpretation: 39% of airports had ticket prices within this range.