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Quantitative Data Analysis: Data Representation (HL)
IB DP Psychology — Research Methods | HL | Paper 3
Learning Intentions By the end of this note, you will be able to:
- Define measures of central tendency (mean, median, mode) and measures of dispersion (range, standard deviation) using IB-aligned terminology.
- Calculate the mean, median, mode, range, and standard deviation from a given data set.
- Explain when each measure of central tendency and dispersion is most appropriate to use, and why.
- Interpret graphical representations of data including bar charts, histograms, scatter plots, and box plots in the context of psychological research.
- Describe the difference between normal and skewed distributions and explain what each implies about a data set.
- Evaluate the strengths and limitations of different methods of data representation using the concept areas of Measurement, Causality, and Bias.
- Apply knowledge of data representation to a stimulus-based research scenario, as required in Paper 3.
- Discuss how the choice of data representation can influence the interpretation of psychological research findings.
Introduction & Context
Imagine a researcher has just finished collecting data from 40 participants in a memory experiment. They have a long column of numbers — reaction times, recall scores, error counts — and they need to make sense of it all. Raw numbers alone tell us very little. A single score of 72 out of 100 means nothing unless we know whether most participants scored around 70, or whether scores ranged wildly from 20 to 95. The challenge of quantitative research is not just collecting numbers — it is organising and presenting them in a way that reveals meaningful patterns.
This is where data representation becomes essential. Psychologists use statistical summaries and visual displays to compress large amounts of information into a form that can be interpreted, compared, and communicated. The choices researchers make about how to represent their data — which average to report, which graph to use, how to show variability — are not neutral. These choices shape what readers see, what conclusions seem justified, and what limitations remain hidden. Understanding data representation is therefore not just a mathematical skill; it is a critical thinking skill that sits at the heart of evaluating psychological research.
🗺️ Analogy — The Weather Summary Think of data representation like a weather forecast summary. A meteorologist doesn't read out every temperature recorded at every weather station across the country — they give you an average, a high, a low, and perhaps a chart. Those summaries are useful, but they also hide information: an average temperature of 18°C could describe a calm spring day or a day where one region hit 30°C while another stayed at 6°C. The same is true in psychology — the summary statistics and graphs we choose reveal some things and conceal others.
Core Concepts
When researchers collect quantitative data, the first question they face is: what is the typical value in this data set? If a psychologist tests the effect of sleep deprivation on reaction time, they want to know what the average reaction time was for each group. But "average" is not a single thing — it is a family of related ideas, each suited to different situations. To choose wisely, we need to understand what each measure actually captures.
📖 Key Definition — Measures of Central Tendency Measures of central tendency are statistical values that describe the centre or typical value of a data set. The three main measures are the mean (the arithmetic average, calculated by summing all values and dividing by the number of values), the median (the middle value when data are arranged in order), and the mode (the most frequently occurring value).
The mean is the most commonly used measure and is calculated by adding all scores together and dividing by the total