CH3-2300

Chapter 3: Central Tendency

Learning Outcomes

  • Understand the purpose of measuring central tendency.

  • Define and compute the three measures of central tendency: mean, median, mode.

  • Describe how the mean is affected when a set of scores is modified.

  • Identify appropriate circumstances for using each measure of central tendency.

  • Explain relationships between the three measures in symmetrical and skewed distributions.

  • Draw and interpret graphs for means or medians representing various treatment conditions or groups.

Key Concepts to Review

  • Summation notation

  • Frequency distributions

3.1 Overview of Central Tendency

  • Central Tendency: A statistical measure to define the center of a distribution, representing a typical score.

  • Purpose: Identify a single score that best captures the overall characteristics of the group.

3.2 The Mean

  • Mean: Calculated by summing all scores and dividing by the number of scores.

    • Three Definitions:

      • Sum of scores divided by the number of scores.

      • Average amount per individual if the total is equally divided.

      • Balance point of the distribution.

The Weighted Mean

  • Used to combine two sets of scores:

    1. Determine combined sum of scores.

    2. Determine total number of scores.

    3. Divide total sum by total count of scores.

Characteristics of the Mean

  • Changing a score affects the mean.

  • Adding/removing a score usually affects the mean unless it equals the mean.

  • Adding or subtracting constants shifts the mean similarly.

  • Multiplying/dividing scores shifts the mean proportionally.

3.3 The Median

  • Median: The middle value when scores are sorted; splits the distribution in half.

  • Continuous Variable Precision: Real limits define the interval for locating the median accurately.

Comparison: Mean vs. Median

  • Mean: Balance point influenced by all scores.

  • Median: Midpoint defined strictly by score counts.

3.4 The Mode

  • Mode: The most frequently occurring score; applicable across any measurement scale.

  • Can have multiple modes in a distribution.

3.5 Selecting a Measure of Central Tendency

  • Mean: Suitable in most cases but sensitive to extreme values.

  • Median: Use when extreme values skew the data.

  • Mode: Ideal for categorical data and skewed distributions.

3.6 Central Tendency and Distribution Shapes

  • Symmetrical Distribution:

    • Mean, median, and mode coincide in value.

    • Can have multiple modes or none at all.

  • Skewed Distribution:

    • Mean shifts toward the tail (positive/negative).

    • Median stays closer to the middle than the mean.

    • Mode is closer to the short tail.

Learning Check & Answers

  • Evaluating statements regarding means, medians, and distribution characteristics.

Key Figures and Graphs

  • Illustrative figures demonstrating mean, median, and their relationships in both symmetrical and skewed distributions.

  • Graphical interpretation of means or medians in practical contexts.