Mathematical Skills (Cambridge (CIE) IGCSE Geography): Revision Note

Mathematical skills in geography

• Some aspects of geography require a range of mathematical skills

• These skills are used for:

  • Calculations

  • Analysing data

Percentages

• Percentages are frequently used in geography

  • 'Percent' simply means 'out of one hundred'

  • For example, 25 of 360 homes in a town were burgled. What is the percentage (to the nearest whole number)?

    • 

• Percentages can be used in many ways, for example, literacy rates or the numbers of people in different age groups in a country

• Percentages can be converted into fractions and back again

  • If 20% of the population cannot read or write, this is 1/5th of the population

Percentage change

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

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

• 

  • In 2020, 25 out of 360 homes in a town were burgled. In 2021, 21 houses were burgled. What is the percentage change?

  • 

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

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

Rounding

• In the example above the answer to 7 divided by 45 is 0.1555

• In geography significant figures can be used to make the numbers easier to work with

• In the example 0.15555 was rounded up to 0.16 to make the calculations easier

• To round up:

  • Identify the digit in the required place value

  • Circle the number to the right of the required place value

    • If the circled number is 5 or more, then you round to the bigger number

    • If the circled number is less than 5, then you round to the smaller number

    • Put a zero in any following place values before the decimal point

Significant figures

• To find the first significant figure when reading from left to right, find the biggest place value that has a non-zero digit

  • The first significant figure of 3097 is 3

  • The first significant figure of 0.0062070 is 6

    • The zeros before the 6 are not significant

    • The zero after the 2 but before the 7 is significant

    • The zero after the 7 is not significant

• Count along to the right from the first significant figure to identify the position of the required significant figure 

  • Do count zeros that are between other non-zero digits

    • E.g. 0 is the second significant figure of 3097

    • 9 is the third significant figure of 3097

  • Use the normal rules for rounding

  • For large numbers, complete places up to the decimal point with zeros

    • E.g. 34 568 to 2 significant figures is 35 000

  • For decimals, complete places between the decimal point and the first significant figure with zeros

    • E.g. 0.003 435 to 3 significant figures is 0.003 44

Proportion

• Direct proportion

  • As one quantity increases/decreases by a certain rate (factor)

  • The other quantity will increase/decrease by the same rate 

• The ratio of the two quantities is constant

  • A map has a scale of 1:25,000 this means that 1 unit on the map (e.g. 1 cm) represents 25,000 units (25,000 cm or 0.25km) in real life

• An inverse proportion means that as one variable increases, the other decreases by a proportionate amount

  • As urban populations increase, rural populations decrease

Ratio

• A ratio is a way of comparing one part of a whole to another

  • Ratios are used to compare one part to another part

What do ratios look like?

• Ratios involve two or three different numbers separated using a colon

  • E.g. 2 : 5,  3 : 1,  4 : 2 : 3 

• Dependency ratios compare the number of dependants (individuals aged 0-14 and over 65) to the working-age population (aged 15-64)

  • In the ratio 2:1, when referring to the dependency ratio this means that for every 2 working-age people there is one dependent person

Magnitude

• In geography the term 'magnitude' has two meanings

• In mathematical skills it is the relative size or scale of a quantity when comparing different geographical data

  • For example, if Country A has a population of 40 million and Country B has a population of 10 million, we can say that Country A's population is four times greater than Country B's

    • This means Country A's population is greater by a magnitude of 4.

• Magnitude can also refer to the amount of energy released in an earthquake

Frequency

• Frequency refers to how often a particular value or category appears within a set of data

• In a traffic survey the number of times each type of vehicle (car, bus, bicycle) passes by is recorded

  • The count of each vehicle type represents its frequency.

• To organise and interpret this data effectively, geographers use frequency tables

• These tables list each category alongside its corresponding frequency, making it easier to identify patterns and trends

  • For example, a frequency table can help to identify the most common mode of transport used in a particular area

Mean, median, mode & range

Mean, median and mode

• These are measures of central tendency

  • Mean = average value

    • The mean is calculated by adding up all of the values in the data set and then dividing by the total number of values in the data set

  • The median is the middle value of a set of data. The numbers are arranged in rank order and then the middle value selected

  • The mode is the value which occurs most frequently in a set of data

Range 

• A measure of dispersion: the spread of data around the average

  • Range is the distance between the highest and lowest value

• Interquartile range is the part of the range that covers the middle 50% of the data