Numerical & Statistical Skills (OCR GCSE Geography)

• A range of numerical skills are needed throughout the final exam papers

Proportion and ratio

• Proportion is relating one part to the whole
  • In a group of 100 if there are 20 people who are 15 and 80 people who are 14
  • The proportion of those 15-year-olds is 20/100 or 20%
• Ratio is the comparison of two quantities 
  • In a group of 100 if there are 20 people who are 15 and 80 people who are 14
  • The ratio is 1:4 so for every person that is 15 there are 4 people who are 14

Magnitude

• Refers to the relative size usually of an event such as an earthquake

Frequency

• Refers to how often something occurs

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

Statistics:

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

Measures of central tendency

• 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
•  

Bivariate data

• Data that consists of 2 variables is called bivariate data
• Data can be either quantitative or qualitative or both 
  • In a river study, bivariate data would be used to show the relationship (correlation) between different river characteristics such as the relationship between the width and depth of the river channel
• The two variables can depend on each other, with one variable influencing the other
• The bivariate data would then have an independent variable and a dependent variable
  • For example, rainfall is an independent variable and runoff is a dependent variable
  • This is because the amount of run-off is dependent on the amount of rainfall, but rainfall is not influenced by run-off
• The relationship between dependent and independent variable can be seen as a positive or negative correlation or relationship
  • A positive correlation means that if the independent variable increases then the dependent would also increase
    • The more it rains, the higher the rate of run-off
  • A negative correlation is when the independent variable increases but the dependent variable decreases
    • Rainfall increased, but the rate of run-off did not
• The relationship (correlation) between two variables (bivariate) is often shown using a scattergraph

Scatter graph

• Scattergraphs are used to show the relationship between two variables
  • Points should not be connected
  • A 'line of best fit' or 'trendline' can be added to show the correlation
    • This is a line or curve that shows the general pattern or direction of the data over time
• Interpolation is where the line of best fit is used for a value that is within the plotted points
• Extrapolation is where the line of best fit is extended beyond the plotted points to gain a future value

Scattergraphs - strengths and weaknesses

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 showing the relationship between width and depth on a river's long profile

Scatter graph to show the relationship between width and depth on a river'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