Water & Carbon Skills (AQA A Level Geography)

Revision Note

Water & Carbon Skills

  • Geographical skills are working skills essential to developing a synoptic approach to answering questions but also observing the 'bigger picture' in geography

Key terms 

  • Quantitative data is measurable and can be expressed by numbers or placed into specific categories

    • Often used to test and prove previously specified concepts or hypotheses

    • Quantitative data is objective as it provides specific values

    • E.g. Barton-on-Sea beach in Dorset, UK is a short 1.75km, 20m wide, shingle and rock beach, backed by high, clay cliffs of between 5-10m

  • Qualitative data is descriptive information, usually written and presents features (quality) in an intuitive way

    • Often used to formulate theories and hypotheses

    • Qualitative data is subjective because it 'describes' from the angle of the viewer

    • E.g. The river is fast and dangerous or the wood is dark and feels dangerous 

  • Primary data is data collected first-hand usually during fieldwork

    • It is real-time data specific to the investigation

    • E.g. Photograph taken of flood defences or species count using a quadrat

  • Secondary data is data collected by others and is used in support of primary data

    • It allows for studies of changes over time - census data collected by the government and compared 

    • E.g. Maps, textbooks, websites, journals etc. 

  • Big data are large datasets that need computational manipulation 

    • Used to show trends, patterns and subsequent links

    • E.g. Geolocation, geospatial data, GIS (geographic information systems), Google Earth, satellite navigation etc. 

  • 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

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

Table Showing Relative Strengths and Limitations of Line Graphs

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

line-graph-River-cross-section

Flow lines

  • Useful for showing the strength of interaction between variables

  • Shows direction and volume along a specific path

  • E.g. the water and carbon cycle use flow lines

  • The lines can also be displayed to show proportion or importance using size or colour to highlight differences 

carbon-cycle-showing-proportional-flow-lines
Image showing carbon cycle proportional flow lines 

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

Table Showing Relative Strengths and Limitations of Compound Graphs

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

example -compound-bar-chart
Image showing data presented on a compound graph

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 of which direction the data should go in

example-triangular-graph

Examiner Tip

In the exam, you will not be asked to draw an entire graph. However, it is common to be asked to complete an unfinished graph using the data provided. You may also be asked to identify anomalous results or to draw the best fit line on a scatter graph.

  • Take your time to ensure that you have marked the data on the graph accurately

  • Use the same style as the data which has already been put on the graph

    • Bars on a bar graph should be the same width

    • If the dots on a graph are connected by a line you should do the same

Mass balance

  • Mass balance is the input, output, and distribution of the water or carbon cycle between its flows/transfers within each stage of the system

  • It accounts for all the material in a process and can be measured locally (a single system) or globally 

    • E.g. a student conducted a mass balance on a drainage basin and they concluded that approximately 84% of the water was directly recycled back to the river while 15% was indirectly returned via plant and sub-surface flows, with the final 1% being removed from the water cycle by deep aquifers

  • A balanced carbon cycle is the outcome of different components working in dynamic equilibrium with each other

    • The atmosphere's carbon composition is partly regulated by ocean and terrestrial photosynthesis

    • Soil health is maintained through decomposition, combustion and carbon storage which is important for ecosystem productivity etc. 

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

Table Showing Relative Strengths and Limitations of Scatter Graphs

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

scattergraph
Scatter graph to show the relationship between width and depth on a river X's long profile

Types of correlation

  • Positive correlation

    • As one variable increases, so too does the other

    • The line of best fit goes from the 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

Examiner Tip

Always check when making calculations what the question has asked you to do. Is it asking for units to be stated or calculate to the nearest whole number or quote to 2 decimal places. 

Worked Example

Making predictions from a set of data

Study Figure 1 below, which shows the cost against distance travelled

scattergraph-example

Figure 1

Predict what the cost at would be at 1.75km

[1 mark]

  • You may be asked to make a prediction for the next step in given data (either table or graph form) in your exam

  • Study the data carefully

  • Look at the direction in which the data is going

  • Are the numbers increasing or decreasing?

  • Is there a clear pattern forming? 

  • E.g. does the data point value change by 3, 4, 6 etc. each time 

Answer:

  • To predict the cost at 1.75 km, find the cost at 1.5 km and 2.0 km

  • Produce a line of best fit to predict the value at 1.75 km

  • Cost would be £1.3 [1]

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?

  • begin mathsize 20px style 25 divided by 360 cross times 100 space equals 6.94 space open square brackets space t o space n e a r e s t space w h o l e space n u m b e r close square brackets space equals 7 percent sign end style

  • A percentage change shows by how much something has either increased or decreased

  • P e r c e n t a g e space c h a n g e space equals fraction numerator f i n a l space v a l u e space minus o r i g i n a l space v a l u e over denominator o r i g i n a l space v a l u e end fraction cross times 100

  • In 2021 only 21 houses were burgled. What is the percentage change in Catland?

  • fraction numerator 21 minus 25 over denominator 25 end fraction cross times 100 equals negative 16 percent sign

  • There has been a decrease of 16% in the rate of burglaries in the Catland area

  • Remember that a positive figure shows an increase but a negative is a decrease

Worked Example

Study Figure 1 and analyse the data presented.

[6 marks]

Figure 1: change in greenhouse gas (GHG) emissions, grouped by relative wealth of country, between 1970 and 2010

fig-1-paper1-june2018-aqa-alevel-geography
  • The best answers will use and manipulate the data; spot trends and anomalies, and make clear connections between different aspects of the data and evidence

Answer:

  • Figure 1 shows that high income countries are still the biggest contributors to GHG production [1] but that there has been little growth between 1990 and 2010 in particular (0.4 Gigatonnes of CO2) [1]. It is upper-middle income countries that have seen the fastest rates of growth of the time periods [1]. For instance, there has been an almost doubling from 9.8 to 18.3 gigatonnes of CO2 produced. Industry appears to have more than doubled in its contribution to GHG in this group of countries (from approximately to 2 to around 5 gigatonnes) [1d].

  • Low and low-middle income countries contribute relatively little to the overall GHG emissions [1], with LICs emissions appear to be shrinking. For instance, combined in 2010 they produced only 11.3 gigatonnes [1], 7.4 gigatonnes less than high income countries [1]. These countries greatest contribution comes through agriculture (especially for low income countries) with very little through energy use and transport [1].

Statistical Skills

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

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 -
fraction numerator bold 184 bold plus bold 90 bold plus bold 159 bold plus bold 142 bold plus bold 64 bold plus bold 64 bold plus bold 95 over denominator bold 7 end fraction bold equals bold 798 over bold 7 bold equals bold 114

  • Median - reordering by size = begin mathsize 22px style 64 space 64 space 90 space stretchy left square bracket 95 stretchy right square bracket space 142 space 159 space 184 end style = 95 is the middle value

  • Mode - only 64 appears more than once

  • Range - 184 space minus space 64 space equals space 120

Upper, lower and inter quartile range

  • These are the values of a quarter (25%) [lower quartile (LQ)] and three-quarters (75%) [upper (UQ)] of the ordered data

No. of shoppers

2

3

6

6

7

9

13

14

17

22

22

 

 

 

Lower quartile

 

 

Median

 

 

Upper quartile

 

 

  • The interquartile range (IQR) is the difference between the upper (UQ) and lower quartile (LQ)

  • It measures the spread (dispersion) of data around the median

  • A large number shows the numbers are fairly spread, whereas, a small number shows the data is close to the median

  • UQ - LQ = IQ [bold 17 bold space bold minus bold space bold 6 bold space bold equals bold space bold 11]

Standard deviation

  • This measures dispersion more reliably than IQR and the symbol for it is 'σ' (sigma)

  • The formula is  bold italic sigma bold space bold equals square root of fraction numerator bold capital sigma bold space stretchy left parenthesis x space minus space x with bar on top stretchy right parenthesis to the power of bold 2 over denominator bold n end fraction end root

  • Σ means 'sum of' and bold x with bold bar on top is another way of writing 'mean' and 'n' is the number of samples taken

  • Work out individual aspects of the formula first e.g. the mean

  • Sample results:

Sample site

1

2

3

4

5

Number of pebbles

5

9

10

11

14

  1. Calculate the mean - begin bold style stretchy left parenthesis 5 plus 9 plus 10 plus 11 plus 14 stretchy right parenthesis end style bold space bold divided by bold space bold 5 bold space bold equals bold space bold 9 bold. bold 8

  2. Calculate begin mathsize 20px style bold italic x bold minus bold x with bold bar on top end style for each number

  3. Square each of those values (the square of a negative number becomes positive)

  4. Add the squared values to give begin mathsize 20px style bold italic capital sigma begin bold style stretchy left parenthesis x minus x with bar on top stretchy right parenthesis end style end style

  5. Divide the total by 'n'

  6. Finally, find the square root

bold italic x

begin mathsize 20px style bold x with bold bar on top end style

bold italic x bold minus bold x with bold bar on top

(x-x¯)

5

9.8

-4.8

23.04

9

9.8

-0.8

0.64

10

9.8

0.2

0.04

11

9.8

1.2

1.44

14

9.8

4.2

17.64

Σ = 42.8

  • σ = 42.85 = 2.93 (2 dp)

  • Numbers closely grouped around the mean shows a small deviation

  • A large standard deviation would show a set of numbers that were spread out

Spearman's rank correlation coefficient

  • A test to determine if two sets of numbers have a relationship

  • Not the easiest to calculate

  • Σ means 'sum of',  d is the difference and 'n' is the number of samples taken

  • The formula is rs = 1 - 6∑d2n3 - n

  1. Rank each number in both sets of data, with the highest number given rank 1, second highest 2 etc.

  2. Calculate 'd' which is the difference between ranks of each group e.g. ranks for group 5 are 4 and 6; difference will be 2

  3. Square value 'd' and calculate the total d2 to find ∑d2

  4. Finally, calculate the coefficient of rs using the above formula

  5. The resulting number should always be between -1 and +1

GNP ($) per capita and Life Expectancy (years)

Country

GNP

Rank

Life Expectancy

Rank

d

d2

1

15,124

5

73

5

0

0

2

20,535

4

72

6

2

4

3

10.432

9

68

8

1

1

4

7,050

11

62

11

0

0

5

22,950

3

76

3

0

0

6

14,800

6

75

4

2

4

7

23,752

2

77

2

0

0

8

36,875

1

79

1

0

0

9

5,525

12

61

12

0

0

10

8,678

10

66

9

1

1

11

12,211

8

65

10

2

4

12

13,500

7

70

7

0

0

n=12

Σd2 = 14

  • Σd2 = 14 and n =12. 

  • rs =1 -6 ×14123 - 12 = 1- 841716 =1-0.048951 (0.05) = 0.95

  • (0.048951 can be rounded to 2 decimal places giving 0.05)

  • A positive result shows a positive correlation, where one variable increases so does the other

  • The closer the number is to 1, the stronger the positive correlation

  • A negative results shows a negative correlation, where one variable increases the other decreases

  • The closer the number is to -1 the stronger the negative correlation

  • If however, the correlation is or near to 0, there is no relationship

Determining significance

  • Spearman's rank may show that two sets of numbers are correlated, however, it does not show how significant the link between the two values are

  • To check for significance; a table of critical values or a graph is needed

  • This looks at the probability of the links occurring by chance 

  • A 5% or higher probability of chance is not significant evidence for a link

  • 1% or less is a significant evidence of a link

  • This is the significance level of a statistical test

  • The degrees of freedom needs calculating - n-2   

    • Using the example above:  12 - 2 = 10 degrees of freedom

    • As rs = 0.95 then the correlation has a less than 1% probability of being by chance

    • Therefore, there is a high significance level of a relationship between GNP and life expectancy

  Spearman’s Rank Correlation Significance Table

Degrees of Freedom

5% (0.05)

1% (0.01)

8

0.72

0.84

9

0.68

0.80

10

0.64

0.77

11

0.60

0.74

12

0.57

0.71

13

0.54

0.69

14

0.52

0.67

15

0.50

0.65

20

0.47

0.59

Examiner Tip

Always check when making calculations what the question has asked you to do. Is it asking for units to be stated or calculate to the nearest whole number or quote to 2 decimal places. 

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