Overview
This lecture covers measures of central tendency—mean, median, and mode—including how to calculate them, when to use each, and their role in statistical research.
Measures of Central Tendency
- Central tendency summarizes where the middle or center of a data distribution lies.
- The main measures are mode, median, and mean.
The Mode
- The mode is the score occurring most frequently in a data set.
- Used mainly with nominal data (categorical variables).
- Distributions can be unimodal (one mode), bimodal (two modes), or multimodal (multiple modes).
The Median
- The median is the middle score at the 50th percentile (half scores above, half below).
- Used for ordinal data or highly skewed interval/ratio data.
- To calculate: order scores; if odd number, pick the middle; if even, average the two center scores.
The Mean
- The mean is the arithmetic average (sum of all scores divided by number of scores, n).
- Used for interval and ratio data, especially with symmetrical distributions.
- In normal distributions, mode, median, and mean are equal; in skewed distributions, the mean shifts towards the skew.
Deviations Around the Mean
- A deviation is the difference between a score and the mean (score minus mean).
- The sum of deviations from the mean is always zero.
- Deviations are used to assess prediction error and variability in statistics.
Population vs. Sample Means
- The population mean uses the symbol μ and includes all members of a population.
- The sample mean is calculated from a smaller group and used to infer the population mean.
Application in Research
- Means help describe groups in experiments (e.g., average memory errors by group).
- Use bar graphs for nominal or ordinal independent variables.
- Sample means are analyzed with statistical tests (t-test, ANOVA) to infer population patterns.
Key Terms & Definitions
- Central Tendency — A measure indicating the center of a data distribution.
- Mode — The most frequently occurring score in a set.
- Median — The score that divides an ordered data set in half.
- Mean — The arithmetic average of a data set.
- Deviation — The difference between an individual score and the mean.
- Population Mean (μ) — The average score for an entire population.
- Sample Mean — The average score from a subset (sample) of the population.
Action Items / Next Steps
- Review calculation procedures for mode, median, and mean.
- Read textbook chapter on central tendency for additional examples.
- Prepare questions on applying measures to class examples for next session.