Graphs, Diagrams & Statistics (AQA GCSE Geography)

Key terminology

Term	Definition
Continuous data	Numerical data that can take any value within a given range, e.g. heights and weights
Discrete data	Numerical data that can only take certain values, e.g. shoe size
Quantitative data	Results that can be expressed using numerical values
Qualitative data	Results that can’t be expressed as numbers, e.g. opinions

Line graph

• One of the simplest ways to display continuous data
• Both axes are numerical and continuous
• Used to show changes over time and space

Strengths	Limitations
Shows trends and patterns clearly	Does not show causes or effects
Quicker and easier to construct than a bar graph	Can be misleading if the scales on the axis are altered
Easy to interpret	If there are multiple lines on a graph it can be confusing
Anomalies are easy to identify	Often requires additional information to be useful

• A river cross-section is a particular form of line graph because it is not continuous data, but the plots can be joined to show the shape of the river channel

Diagram showing the use of a line graph

Bar chart

• A bar chart is the simplest form of displaying data
• Each bar is the same width, but can have varying lengths
• Each bar is drawn an equal distant apart (equidistant)
• The data is discrete data
• Bar graphs are useful for:
  • Comparing classes or groups of data
  • Changes over time

Strengths	Limitations
Summarises a large set of data	Requires additional information
Easy to interpret and construct	Does not show causes, effects or patterns, can be too simplistic
Shows trends clearly	Can only be used with discrete data

A typical bar graph presentation

Histograms

• Histograms show continuous data
• Always use a ruler to draw the bars
• All bars should be the same width 
• The top of the bar should reach the number on the side of the graph that is being represented
• There should be no gaps, all bars should be touching

• Ensure all axes are labelled and that the graph has a title

Strengths	Limitations
Large data sets can be graphed easily	They can only be used for numerical data
You can compare data	Can be difficult to pinpoint exact data values

A diagram of a typical histogram

Compound or divided bar chart

• The bars are subdivided to show the information with all bars totalling 100%
• Divided bar charts show a variety of categories

• They can show percentages and frequencies

Strengths	Limitations
A large amount of data can be shown on one graph	A divided bar chart can be difficult to read if there are multiple segments
Percentages and frequencies can be displayed on divided bar char	Can be difficult to compare sometimes

Diagram showing a compound bar graph

Population pyramid

• A type of histogram
• Used to show the age-sex of a population
• Can be used to show the structure of an area/country
• Patterns are easy to identify

Strengths	Limitations
Easy to compare age and sex data	Can take a long time to construct
Easy to read and annotate	Detail can be lost in the data (figures just show a cohort); additional annotations may be necessary

Diagram showing a typical population pyramid

Pie chart

• Used to show proportions, the area of the circle segment represents the proportion
• A pie chart can also be drawn as a proportional circle 
• Pie charts can be located on maps to show variations at different sample sites
• Percentage of pie chart must add to 100%
• To calculate degrees of the pie chart (which totals 360°) divide the percentage by 100 and then multiply by 360
• Each segment should be a different colour

Strengths	Limitations
Clearly shows the proportion of the whole	Does not show changes over time, hard to compare two sets of data
Easy to compare different components	Difficult to understand without clear labelling
Easy to label	Calculating the size of each section can be difficult
Information can be highlighted by separating segments	Can only use for a small number of categories otherwise lots of segments become confusing

Diagram showing a pie chart

Pie Chart Showing Energy Sources in an Area

Rose diagram

• Use multidirectional axes to plot data with bars
• Compass points are used for the axis's direction
• Can be used for data such as wind direction, noise or light levels

A rose diagram 

Wind direction shown on a rose diagram

Triangular graph

• Have axes on three sides all of which go from 0-100
• Used to display data which can be divided into three
• The data must be in percentages 
• Can be used to plot data such as soil content, employment in economic activities
• Read each side carefully so you are aware which direction the data should go in

A triangular graph diagram

Choropleth map

• Maps which are shaded according to a pre-arranged key
• Each shade represents a range of values
• It is common for one colour in different shades to be used
• Can be used for a range of data such as annual precipitation, population density, income levels, etc...

Strengths	Limitations
The clear visual impression of the changes over space	Makes it seem as if there is an abrupt change in the boundary
Shows a large amount of data	Distinguishing between shades can be difficult
Groupings are flexible	Variations within the value set are not visible

A choropleth diagram 

Proportional symbols map

• The symbols on the map are drawn in proportion to the variable represented
• Usually, a circle or square is used but it could be an image
• Can be used to show a range of data, for example, population, wind farms and electricity they generate, traffic or pedestrian flows

Strengths	Limitations
Illustrates the differences between many places	Not easy to calculate the actual value
Easy to read	Time-consuming to construct
Data is specific to particular locations	Positioning on a map may be difficult, particularly with larger symbols

Diagram showing proportional symbols

Proportional Circles Map Showing GDP (Billion US$) across Europe

Pictograms

• These are a way of displaying data using symbols or diagrams drawn to scale
• Useful way of showing data if accuracy is not too important and data is discrete
• Years do not need to be continuous
• Symbols do not need to be whole but can represent a proportion
• A key is needed to show if the total number of objects or events that image represents exceeds one

How to read a pictogram

• Step 1: Read the problem carefully and identify the specific information requested from the pictograph
• Step 2: Count the symbols corresponding to the desired information and report the count

Pictogram showing symbols 

• In the pictogram above, you can see that 4 shoppers walked to the supermarket, but only one used a taxi
• The majority of shoppers used a car to travel to the supermarket

Statistics:

• This is the study and handling of data, which includes ways of gathering, reviewing, analysing, and drawing conclusions from data

Scatter graph

• Points should not be connected
• The best fit line can be added to show the relations
• Used to show the relationship between two variables
  • In a river study, they are used to show the relationship between different river characteristics such as the relationship between the width and depth of the river channel

Strengths	Limitations
Clearly shows data correlation	Data points cannot be labelled
Shows the spread of data	Too many data points can make it difficult to read
Makes it easy to identify anomalies and outliers	Can only show the relationship between two sets of data

Scatter graph to show the Relationship Between Width and Depth on a River Long Profile

Types of correlation

• Positive correlation
  • As one variable increases, so too does the other
  • The line of best fit goes from bottom left to the top right of the graph
• Negative correlation 
  • As one variable increases the other decreases

  • The line of best fit goes from the top left to the bottom right of the graph

• No correlation
  • Data points will have a scattered distribution
  • There is no relationship between the variables

Mean, median, mode and range

• Mean = average value (all the values added and divided by the number of items)
• Median = middle value when ordered in size
• Mode = most common value
• Range = difference between the highest value and lowest value

Sample site	1	2	3	4	5	6	7
Number of pebbles	184	90	159	142	64	64	95

• Taking the example above to calculate:
• Mean:
• Median: reordering by size = = 95 is the middle value
• Mode: only 64 appears more than once
• Range -

Upper and lower quartiles

• These are the values of a quarter (25%) and three-quarters (75%) of the ordered data

Number of shoppers	2	3	6	6	7	9	13	14	17	22	22
			Lower quartile			Median			Upper quartile

• The interquartile range is the difference between the upper and lower quartile
•  

Percentage and percentage change

• To give the amount A as a percentage of sample B, divide A by B and multiply by 100
  • In 2020, 25 out of 360 homes in Catland were burgles. What is the percentage (to the nearest whole number) of homes burgled?
  • 

• A percentage change shows by how much something has either increased or decreased
• 
  • In 2021 only 21 houses were burgled. What is the percentage change in Catland?
  • 
  • There has been a decrease of 16% in the rate of burglaries in the Catland area
• Do remember that a positive figure shows an increase but a negative is a decrease