AP Psychology · Lesson 6 of 9 · Science practices

Descriptive statistics: central tendency, variation, percentile rank and the normal curve

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Descriptive statistics organize and summarize raw research data into clear, meaningful numbers. On the AP Psychology exam, you will calculate and interpret these values without a calculator in Section I data sets and explain what they mean in context on the Article Analysis Question (AAQ) Part C.

By the end you’ll be able to

Calculate the mean, median, mode and range of a small data set by hand.
Interpret the mean, median, mode, range, standard deviation and percentile rank of a data set in the context of a study.
Explain the normal curve, including the percentages of scores within one, two and three standard deviations of the mean (about 68%, 95% and 99.7%).
Interpret positively and negatively skewed distributions, including how extreme scores pull the mean away from the median, and interpret bimodal distributions.

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Core ideas (continued)
Worked examples
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What the exam asks

Section I (Multiple Choice): You will compute the mean, median, mode, and range of small data sets by hand, compare groups using standard deviation, find percentile ranks using the normal curve ( $68\%\text{–}95\%\text{–}99.7\%$ ), and identify skewed or bimodal distributions.
Section II (AAQ Part C): You will explain what a specific descriptive statistic (such as a mean or standard deviation) indicates about the participants or variables in the context of the study, going beyond simply repeating the numbers.

Core ideas

Measures of central tendency

A measure of central tendency uses a single score to represent the center or typical value of a data set.

Measure	How to find it	When to use it / Exam feature
Mean	Add all scores and divide by the number of scores ( $N$ ): $\text{Mean} = \frac{\sum X}{N}$	Best for symmetrical distributions. Easily distorted by extreme scores (outliers), which pull the mean toward the tail.
Median	Put scores in numerical order and find the exact middle score (if $N$ is even, average the two middle scores).	Best for skewed distributions because outliers do not distort it (e.g., household income or reaction times with a few distractions).
Mode	The most frequently occurring score(s) in a data set.	Best for categorical data or identifying a bimodal distribution (two distinct peaks, often indicating two subgroups in the sample).

Measures of variation

Variation describes how similar or spread out the scores are around the center.

Range: The gap between the highest and lowest scores: $\text{Range} = \text{Maximum} - \text{Minimum}$ Because it uses only two numbers, a single outlier drastically inflates the range.
Standard deviation ( $SD$ ): A measure of the average distance that scores vary from the mean. You will never calculate $SD$ $S D$ by hand on the exam, but you must interpret it:
- A small means scores are clustered tightly near the mean (participants responded very similarly).

Skewed distributions

When a distribution is lopsided, the tail (not the tall peak) names the skew, and the outliers in that tail pull the mean away from the median:

Positively skewed (right-skewed): A few unusually high scores create a long tail to the right. Here, $\text{Mean} > \text{Median} > \text{Mode}$ .
Negatively skewed (left-skewed): A few unusually low scores create a long tail to the left. Here, $\text{Mean} < \text{Median} < \text{Mode}$ .

SD