Mathematical Content & Computation (AQA GCSE Psychology): Revision Note
Exam code: 8182
Decimal & standard form
Decimals are any numbers which include a decimal point, for example:
6.31
20.059
468.27
The digits before the decimal point are whole numbers; the digits after the decimal point are parts of that whole number, e.g.
6.31: the 6 in this number refers to 6 units; 3 in this number refers to 3 tenths
20.059: the 2 refers to two tens; the 5 refers to 5 hundredths, and the 9 refers to 9 thousandths
468.27: the 4 refers to 4 hundreds; the 2 refers to 2 tenths
Standard form is a way of dealing with very large (or very small) numbers without calculations becoming too cumbersome, e.g.
10 to the power of 2 = 100, which is written as 10² (i.e., it refers to 10 x 10)
835,000,000,000 = 8.35 × 1011 in standard form (835 must be reduced to a number between 1 and 10, and then 10 ‘to the power of’ is added to express the size of the number)
Small numbers can also be written in standard form
In this case the index (the ‘to the power of’ number) must be negative, e.g.
0.000000000000761 is written as 7.61 × 10⁻¹³
Examiner Tips and Tricks
You can read more about standard form in our maths pages here.
Fractions & ratios
Fractions enable researchers to see parts of the whole in terms of the data set they have collected, e.g.
5 out of 25 participants scored above 100 in a concentration task = 5/25
20 out of 50 participants stated that purple was their favourite colour = 20/50
Fractions should be reduced to their simplest form, which is done by finding the highest common factor between the top number (the numerator) and bottom number (the denominator) and dividing both by that factor, e.g.
5/25 = 1/5 (5 is the common factor; it divides equally into 5 and 25)
20/50 = 2/5 (10 is the highest common factor)
To change a fraction into a decimal, divide the numerator by the denominator, e.g.
1/5 = 1 ÷ 5 = 0.2
2/5 = 2 ÷ 5 = 0.4
Ratios enable researchers to compare quantities as proportions of the whole data set, e.g.
5 out of 25 participants scored above 100 in a concentration task = 5:25
20 out of 500 participants stated that purple was their favourite colour = 20:50
As with fractions, ratios should be reduced to their simplest form, e.g.
5:25 = 1:5
20:50 = 2:5
Examiner Tips and Tricks
Before writing a ratio, always check what is being compared in the question.
If the question asks for the ratio of one group to another group (e.g. “A compared to B”), this is a part-to-part ratio
If the question asks for the ratio of one group to the total (e.g. “out of the total sample”), this is a part-to-whole ratio
If the question asks for the ratio of one group to everyone else (e.g. “did X compared to did not”), this is a part-to-remainder ratio
In AQA GCSE Psychology, students are most commonly asked to calculate part-to-part ratios, usually comparing two groups or conditions directly (e.g. Group A compared to Group B).
Always follow the order given in the question, as this determines the order of the ratio.
Percentages
Percentage refers to a number or quantity calculated as a proportion out of 100, e.g.
65%
3%
18%
Percentages can be expressed as a fraction or a decimal, e.g.
65% as a decimal is 0.65; as a fraction it is 13/20
3% as a decimal is 0.03; as a fraction it is 3/100
To calculate the percentage from a data set, the numerator is multiplied by 100 and then divided by the denominator, e.g.
63 out of 70 participants chose A:
63 x 100 = 6300 ÷ 70 = 90%
15 out of 82 participants scored below average:
15 x 100 = 1500 ÷ 82 = 18.29%
Significant figures & estimating results
Significant figures is another way of dealing with very large (or very small) numbers
A very large number can be rounded to the nearest round number (a number that ends with a 0), e.g.
596,321 rounded to one significant figure = 600,000
341,602 rounded to one significant figure = 300,000
For numbers with a decimal point, it is the digits after the decimal point that may be rounded up or down, depending on the number of significant figures required, e.g.
0.00038967 to two significant figures = 0.00039
0.0000578 to two significant figures = 0.000058
A common mistake made by students is confusing decimal places with significant figures:
Decimal places are rounded from just after the decimal point
Significant figures are rounded from the first non-zero digit, wherever it appears in the number
Estimating results can be done by rounding numbers up or down before carrying out a calculation, e.g.
619 × 280 could be estimated as 600 × 300
Worked Example
Here is an example of a question you might be asked on this topic - for AO2.
AO2: You need to apply your knowledge and understanding, usually referring to the ‘stem’ in order to do so (the stem is the example given before the question)
Jenny Kellog conducts a survey at her sixth-form college to investigate which breakfast cereal students prefer. She uses a sample of 60 students, 18 of whom express a preference for Crunchy Nut Cornflakes.
Question: Calculate the percentage of students who stated a preference for Crunchy Nut Cornflakes. Show your workings. [2]
Model answer:
30% of the students stated a preference for Crunchy Nut Cornflakes
This is calculated as 18 × 100 = 1800 ÷ 60 = 30%
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