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Descriptive Statistics
IB DP Psychology — Data Analysis and Interpretation | HL | Paper 3
Learning Intentions By the end of this note, you will be able to:
- Define descriptive statistics, measures of central tendency, and measures of dispersion using IB-aligned terminology.
- Explain the difference between the mean, median, and mode, and identify when each is the most appropriate measure to use.
- Calculate the mean, median, mode, range, and standard deviation from a given data set.
- Interpret what measures of central tendency and dispersion reveal about a data set in a psychological research context.
- Distinguish between normal and skewed distributions and explain how skew affects the choice of central tendency measure.
- Evaluate the strengths and limitations of different descriptive statistics using relevant concept areas including Measurement, Causality, and Bias.
- Apply descriptive statistics to interpret findings from psychological research studies in Paper 3 source-based questions.
- Analyse a given data set or research scenario using appropriate descriptive statistical tools and justify your choices.
Introduction & Context
Imagine a psychology researcher has just finished collecting data from 40 participants on how many hours of sleep they got the night before an exam. She has a column of 40 numbers ranging from 3 to 10. What does she do with them? Simply listing all 40 values tells us very little — the human brain cannot easily extract meaning from a raw list of numbers. What the researcher needs is a way to summarise the data: to capture its essential character in just a few meaningful figures.
This is exactly what descriptive statistics do. Rather than inferring things about populations or testing hypotheses, descriptive statistics simply describe what is already in the data. They compress a large, unwieldy set of numbers into a small number of meaningful summaries — telling us where the data tends to cluster, how spread out it is, and what shape it takes. For any psychologist reading a research paper or designing a study, understanding these tools is not optional — it is the foundation of data literacy.
In IB Psychology Paper 3, you will be given a research scenario and asked to interpret, justify, and evaluate the statistical choices made by the researchers. This note equips you with the conceptual understanding and practical skills to do exactly that.
🎯 Analogy — The Weather Forecast Think of descriptive statistics like a weather summary. Rather than listing the exact temperature at every minute of every day in a month, a meteorologist gives you the average temperature, the highest and lowest values, and whether the weather was consistent or variable. These summaries do not tell you everything — but they give you the most important information in a form you can actually use. Descriptive statistics do the same for psychological data.
Core Concepts
Before we can evaluate or interpret any psychological data, we need to understand what kind of summary we are looking at. Descriptive statistics fall into two broad families: those that tell us about the typical or central value in a data set, and those that tell us how spread out the values are around that centre. Both families are necessary — knowing only the average without knowing the spread, or vice versa, gives an incomplete picture.
📖 Key Definition — Descriptive Statistics Descriptive statistics are numerical summaries that organise, simplify, and describe the key features of a data set. They do not allow researchers to draw conclusions beyond the data collected, nor do they test hypotheses — they simply describe what is present in the sample.
Descriptive statistics are always the first step in data analysis. Before any inferential test is run, a researcher should examine the central tendency and dispersion of their data. These summaries also appear in the results sections of published studies, and in Paper 3 you will be expected to