Graphs, Diagrams & Statistics (AQA GCSE Geography): Revision Note

Graphs & diagrams

Key terminology

• 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

  

  • 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

• Strengths

  • Shows trends and patterns clearly

  • Quicker and easier to construct than a bar graph

  • Easy to interpret 

  • Anomalies are easy to identify

• Limitations

  • 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

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 distance apart (equidistant)

• The data is discrete data

• Bar graphs are useful for:

  • Comparing classes or groups of data

  • Changes over time

• Strengths

  • Summarises a large set of data 

  • Easy to interpret and construct

  • Shows the trends clearly

• Limitations

  • Requires additional information

  • Does not show causes, effects or patterns; can be too simplistic

  • Can only be used with discrete data

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

  • Large data sets can be graphed easily

  • You can compare data

• Limitations

  • They can only be used for numerical data

  • Can be difficult to pinpoint exact data values

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

  • A large amount of data can be shown on one graph

  • Divided bar charts can display percentages and frequencies

• Limitations

  • Can be difficult to compare sometimes

  • A divided bar chart can be difficult to read if there are multiple segments 

Population pyramid

• A type of histogram that is 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

  • Easy to compare the age and sex ratios

  • Easy to read and annotate

• Limitations

  • Can take a long time to construct

  • Detail can be lost in the data (figures just show a cohort)

  • Additional annotations may be necessary

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

• The percentages in 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

  • Clearly shows the proportion of the whole

  • Easy to compare different components

  • Easy to label

  • Information can be highlighted by separating segments

• Limitations

  • Does not show changes over time; hard to compare two sets of data

  • Difficult to understand without clear labelling

  • Calculating the size of each section can be difficult 

  • Can only be used for a small number of categories; otherwise, lots of segments become confusing

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 

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 and employment in economic activities

• Read each side carefully so you are aware which direction the data should go in

• The exam will not require you to draw a complete graph

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

  • The clear visual impression of the changes over space

  • Shows a large amount of data

  • Groupings are flexible 

• Limitations

  • Makes it seem as if there is an abrupt change in the boundary

  • Distinguishing between shades can be difficult

  • Variations within the value set are not visible

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

  • Illustrates the differences between many places

  • Easy to read

  • Data is specific to particular locations

• Limitations

  • Not easy to calculate the actual value

  • Time-consuming to construct

  • Positioning on a map may be difficult, particularly with larger symbols

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

  • Clearly shows data correlation

  • Shows the spread of data

  • Makes it easy to identify anomalies and outliers

• Limitations

  • Data points cannot be labelled

  • Too many data points can make it difficult to read

  • Can only show the relationship between two sets of data

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

• Taking the example above to calculate:

• Mean:

• Median: reordering by size = 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

• Lower quartile is 6

• Median is 9

• Upper quartile is 17

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

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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 burgled. 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