Mathematical Skills » Statistical Measures - Mean, Mode, Median

What you'll learn this session

Study time: 30 minutes

How to calculate the mean, median and mode in geographical data
When to use different statistical measures in geography
How to interpret statistical measures in geographical contexts
Practical applications of statistical measures in geographical fieldwork
How to represent statistical data visually

Introduction to Statistical Measures in Geography

Geography isn't just about maps and countries - it involves lots of data! When studying patterns in population, climate, development, or migration, geographers need to make sense of large sets of numbers. This is where statistical measures come in handy. They help us summarise data and spot important trends.

Key Definitions:

Statistical measures: Mathematical calculations that summarise data to help identify patterns, trends and relationships.
Mean: The average value, calculated by adding all values and dividing by the number of values.
Median: The middle value when all data is arranged in order.
Mode: The most frequently occurring value in a dataset.
Range: The difference between the highest and lowest values in a dataset.

📊 Why Statistics Matter in Geography

Statistics help geographers to:

Summarise large datasets into manageable information
Compare different places or time periods
Identify patterns and anomalies
Test hypotheses and theories
Make predictions about future trends

📝 Common Data in Geography

You'll encounter statistics in many areas:

Population figures
Climate data (temperature, rainfall)
Development indicators (GDP, literacy rates)
River discharge measurements
Land use surveys
Migration statistics

The Mean (Average)

The mean is what most people think of as the "average." It's calculated by adding up all the values in a dataset and dividing by the number of values.

How to Calculate the Mean

Formula: Mean = Sum of all values ÷ Number of values

Example: Calculating Mean Rainfall

Monthly rainfall in Cambridge (mm): 45, 35, 40, 50, 55, 30, 25, 35, 40, 60, 55, 50

Sum of values: 45 + 35 + 40 + 50 + 55 + 30 + 25 + 35 + 40 + 60 + 55 + 50 = 520

Number of values: 12 months

Mean rainfall: 520 ÷ 12 = 43.3 mm

This tells us that, on average, Cambridge receives 43.3 mm of rainfall per month.

Strengths of the Mean

Uses all data values in the calculation
Widely understood and recognised
Useful for comparing different datasets

Limitations of the Mean

Can be skewed by extreme values (outliers)
Doesn't always represent a "typical" value
Can give a value that doesn't actually exist in the dataset

The Median

The median is the middle value when all data is arranged in order from lowest to highest. If there's an even number of values, the median is the average of the two middle values.

How to Calculate the Median

Steps:

Arrange all values in ascending order (lowest to highest)
If there's an odd number of values, the median is the middle value
If there's an even number of values, the median is the average of the two middle values

Example: Finding the Median Temperature

Daily maximum temperatures in July (°C): 24, 26, 23, 28, 32, 25, 27

Arranged in order: 23, 24, 25, 26, 27, 28, 32

There are 7 values (odd number), so the median is the 4th value: 26°C

This tells us that half the days were cooler than 26°C and half were warmer.

Strengths of the Median

Not affected by extreme values or outliers
Represents the "middle" of the dataset
Better than the mean for skewed distributions

Limitations of the Median

Doesn't use the actual values of all data points
Can be less useful for further statistical analysis

The Mode

The mode is the value that appears most frequently in a dataset. It shows what's most common or typical.

How to Identify the Mode

Simply count how many times each value appears and identify which occurs most often.

Example: Finding the Modal Land Use

Land use categories in a survey (30 sample points):

Residential: 12 points

Commercial: 8 points

Industrial: 5 points

Recreational: 3 points

Agricultural: 2 points

The mode is "Residential" as it appears most frequently (12 times).

Strengths of the Mode

Shows the most common value
Works well for categorical data (like land use types)
Not affected by extreme values
Easy to identify visually

Limitations of the Mode

Some datasets have no mode (if all values appear equally often)
Some datasets have multiple modes
Not always representative of the entire dataset

📈 Mean

Best when:

Data is evenly distributed
There are no extreme values
You need a precise average

Example: Average annual rainfall

📏 Median

Best when:

Data has outliers
Distribution is skewed
You need a "middle" value

Example: Household incomes in a region

📊 Mode

Best when:

You need the most common value
Working with categorical data
Looking for the "typical" case

Example: Most common land use type

Practical Applications in Geography

Using Statistical Measures in Fieldwork

When conducting geographical fieldwork, statistical measures help you make sense of your collected data:

🌊 River Studies

When measuring river characteristics:

Mean depth can show the average water level
Median velocity helps understand typical flow speed
Modal pebble size indicates dominant sediment type
Range of discharge shows variation between seasons

🌇 Weather Studies

When analysing climate data:

Mean temperature shows average conditions
Median rainfall helps identify typical precipitation
Modal wind direction shows prevailing winds
Range of temperatures indicates climate variability

Case Study Focus: Urban Temperature Survey

Students in Birmingham conducted an urban heat island study, measuring temperatures at 20 locations from the city centre to rural areas.

Results:

Mean temperature: 18.7°C
Median temperature: 19.1°C
Mode temperature: 20.0°C
Range: 5.2°C (from 16.3°C to 21.5°C)

Interpretation: The mean is lower than the median, suggesting some cooler outliers (rural areas). The mode being higher than both mean and median indicates that temperatures of 20°C were most common, likely in the built-up areas. The range shows significant temperature variation across the study area, supporting the urban heat island theory.

Representing Statistical Data

Once you've calculated statistical measures, you'll need to present them effectively:

📈 Graphs and Charts

Different visualisations work best for different measures:

Line graphs: Show means over time (e.g., temperature trends)
Bar charts: Good for comparing means between different places
Histograms: Can show the distribution, with mode as the highest bar
Box plots: Show median, range and quartiles together

💡 Tips for Effective Data Presentation

Always include units of measurement
Label axes clearly
Include a title that explains what the data shows
Consider adding the statistical measures to your visualisation
Use appropriate scales to avoid misleading representations

Exam Tips: Statistical Measures

✅ Exam Success Strategies

Show all your working when calculating statistical measures
Always include units in your answer (e.g., mm, °C, people/km²)
Explain why you've chosen a particular measure for your data
Interpret what the statistical measure tells you about the geographical pattern
Be prepared to calculate means, medians and modes in the exam
Practice with different types of geographical data
Remember that sometimes you'll need to use more than one measure to fully describe a dataset

Summary

Statistical measures are essential tools for geographers to make sense of data. The mean gives an average using all values, the median shows the middle value and the mode identifies the most common value. Each has its strengths and limitations and choosing the right measure depends on your data and what you want to show. By mastering these basic statistical measures, you'll be better equipped to analyse geographical patterns and support your findings with evidence.

🧠 Test Your Knowledge!