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Descriptive Statistics

The Role of Summarization

Introduction to Descriptive Statistics

Descriptive statistics summarise, organise, and describe data in a meaningful way, helping to understand patterns without drawing conclusions beyond the data. Key descriptive statistics include mean, median, mode, and range.

Central Tendency: Mean (Average)

1

Definition & Calculation

The mean is the arithmetic average of all data points in a set. Calculation: Add all values, then divide by the total number of values. Example: Data set: 4, 6, 8, 10; Mean = (4+6+8+10)/4 = 7.
2

Usefulness

Provides a single value representing the central point in data. Commonly used in psychology when data is evenly distributed.
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Weakness

Sensitive to outliers (extreme values can skew the mean).

Central Tendency: Median (Middle Value)

1

Definition

The median is the middle value when the data is arranged in order.
2

Calculation Steps

Rank data from smallest to largest. If odd, the median is the middle number. If even, it is the average of the two middle numbers. Example (Even data): 3, 5, 7, 9; Median = (5+7)/2 = 6.
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Usefulness

Not affected by outliers. Good for skewed distributions.

Mode and Range: Key Concepts

These measures quickly summarize frequency (Mode) and overall spread (Range) within the data set.

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Mode

The most frequently occurring value in a data set. Useful for categorical data where mean or median cannot be calculated. (Example: 2, 3, 3, 4, 5; Mode = 3).
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Range

Measures the spread between the highest and lowest data points. Calculation: Range = Highest value − Lowest value. (Example: 10 − 2 = 8).

Measure Selection Guide

Understanding which measure is 'best' depends entirely on the nature and distribution of your data.

Measure Best for... Limitations
Mean Symmetrical, normally distributed data sets Affected by outliers or skew
Median Skewed distributions or ordinal data Does not use all data values
Mode Nominal or categorical data; identifying common outcomes May be multiple or none
Range Quickly assessing spread or dispersion Can be distorted by extreme values

Examples in Psychological Research

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Mean: Average IQ score in a group.
Median: Median time taken to complete a task when outliers present.
Mode: Most common favourite colour in a sample.
Range: Spread in ages of participants.

Descriptive Statistics Deck
Term
Mean

What is the mean in descriptive statistics?

Answer
Definition

The arithmetic average of all data points in a set.

Term
Median Calculation

How do you calculate the median?

Answer
Method

Arrange data in order and find the middle value; if even number of data points, average the two middle numbers.

Term
Mode Use

When is the mode most useful?

Answer
Use Case

For categorical data or to identify the most frequent value.

Term
Range Calculation

How is the range calculated?

Answer
Formula

Range = Highest value − Lowest value.

Term
Mean Limitation

What is a key limitation of the mean?

Answer
Limitation

It is sensitive to outliers.

Term
Median vs Mean

Why use the median instead of the mean?

Answer
Reason

Because the median is not affected by outliers and is better for skewed distributions.

Term
Range Meaning

What does the range tell us about a data set?

Answer
Meaning

It shows the spread or dispersion between the highest and lowest values.

Term
Multiple Modes

Can a data set have more than one mode?

Answer
Explanation

Yes, this is called bimodal or multimodal data.

Term
Best Measure for Normal Data

Which measure is best for symmetrical, normally distributed data?

Answer
Measure

The mean.

Term
Mode Example in Psychology

What is an example of using the mode in psychology?

Answer
Example

Finding the most common favourite colour in a sample.

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📊 Statistics Quiz: Measures of Central Tendency

1. Which measure of central tendency is most affected by extreme values?

The mean uses all values and is sensitive to outliers, which can skew the average.

2. If a data set is skewed, which measure is usually preferred?

The median is not affected by skewness or extreme values and better represents the center in skewed data.

3. What does the mode represent in a data set?

Mode is the value that occurs most often.

4. How do you calculate the range?

Range measures the spread between extremes in the data.

5. For nominal data, which measure is most appropriate?

Nominal data categories can only be described by the mode because mean or median cannot be calculated.

📊 Results

  • Notes and Quiz
  • Psychology
  • GCSE
  • Mental Health
  • AQA