Lecture Notes: Analyzing Frequency Tables

Introduction to Frequency Tables

• Definition: A frequency table displays data about occurrences of specific values (e.g., doctor's visits).
• Purpose: Shows how often a particular event or score occurs.
• Example: Doctor's visits frequency over a 3-month period.
  • Data: Number of visits and number of people who made that many visits.
  • Example data points:
    • 5 people did not visit the doctor.
    • 6 people visited once.
    • 14 people visited twice.

Key Concepts in Frequency Analysis

Total Number of People Surveyed

• Objective: Calculate the total number of people.
• Method: Sum the frequency column.
• Calculation:
  • Add frequencies: 5 + 6 + 14 + ... = 34.
• Result: 34 people surveyed.

Median Calculation

• Definition: The median is the middle value in an ordered set of data.
• Steps:
  1. Arrange data in ascending order (already done).
  2. Determine if the number of scores is odd or even.
  3. For 34 scores (even), the median is between the 17th and 18th scores.
  4. Count frequencies to locate the median.
• Result: Median is within the group of people who visited 2 times.

Mean Calculation

• Symbol: Represented by ( \overline{X} ).
• Objective: Calculate the average visits.
• Steps:
  1. Create an additional column for frequency multiplied by number of visits (F ( \times ) visits).
  2. Sum this column to get total visits.
  3. Divide total visits by the total number of people.
• Calculation:
  • Total visits: 71.
  • Mean = 71/34 = 2.08 (approx.).
• Observation: Close to 2 because most people visited twice.

Mode

• Definition: The value that appears most frequently.
• Result: Mode is 2, as most people visited twice.

Range

• Definition: Difference between the highest and lowest values.
• Calculation:
  • Top value (8 visits) - Bottom value (0 visits) = 8.
• Result: Range is 8.

Summary

• Frequency table: Useful for understanding data distribution.
• Core metrics: Median, mean, mode, and range provide insights into data tendencies and variances.
• Frequency analysis techniques: Highlighted methods for calculating key statistical measures.