Descriptive Statistics in Psychology

Sample vs. Population

• Entire populations (N) are often impractical to study; research typically uses samples (n).

• Larger samples are preferred but may not always be possible (e.g., studying rare conditions).

Descriptive Statistics Overview

• Techniques for organizing, summarizing, and interpreting sample data.

• Frequency: Number of observations in a category. Often visualized with bar plots or histograms.

Data Distributions

• Normal Distribution: Centered around a point; examples include height, weight, IQ.

• Skewed Distributions:

  • Negative skew: Tail to the left.

  • Positive skew: Tail to the right.

  • Skew direction indicates limits in data.

Measures of Central Tendency

• Central Tendency: Describes where data cluster.

• Mean: Sum of data points divided by the number of points.

• Median: Midpoint; 50% of observations on either side.

• Mode: Most frequent observation; primarily used for categorical data.

Equality in Normal Distribution

• In a normal distribution, mean, median, and mode are equal.

• Use median for skewed data distributions (e.g., income).

Variability in Data

• Variability indicates how scores differ from mean/median.

  • Low variability: Scores are similar.

  • High variability: Scores cluster around extremes.

• Standard Deviation (s): Average distance of scores from the mean.

  • 68% of data within +/- one standard deviation; 95.2% within 2 standard deviations.

Examples and Conclusions

• IQ scores: Mean = 100, SD = 15. A score of 130 is above 97% of the population.

• Inferences from data are probabilistic.