Mathematical Content (AQA AS Psychology)

Percentages 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% 

An alternative method is to divide the numerator by the denominator and then multiply by 100

• 63 out of 70 participants chose A = 63 ÷ 70 = 0.9 x100 = 90%

• 15 out of 82 participants scored below average = 15 ÷ 82 = 0.18.29 x 100 = 18.29%

Decimals are any numbers which include a decimal point, e.g.

• 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 in this number refers to two tens; the 9 refers to 9 hundredths

• 468.27 - the 4 in this number refers to 4 hundreds; the 2 in this number refers to 2 tenths

Decimal place refers to the position of a digit to the right of the decimal point

Numbers with several digits after the decimal point can be rounded up or down to a specific number of decimal places e.g.

• if the number is 276.985 it can be rounded up to 276.99 as the final number 5 means that the 8 is rounded up to a 9

• if the number is 276.983 it can be rounded down to 276.98 as the final number 3 is less than 5 so the 8 remains in place

• rounding up or down to decimal places refers to the number of digits after the decimal point

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

• 16 out of 100 participants stated that purple was their favourite colour = 16/100

Fractions should be reduced to their simplest form which is done by finding the highest common factor between the top (the numerator) and bottom number (the denominator) and dividing them by the factor, e.g.

• 5/25 = 1/5 (5 is the common factor; it divides equally into 5 and 25)

• 16/100 = 4/25 (4 is the highest common factor as 16 does not divide equally into 100)

A fraction can be converted into a decimal number by dividing the numerator by the denominator e.g.

• 1/5 is 1 ÷ 5 = 0.02

• 4/25 is 4 ÷ 25 = 0.16

Ratios enable researchers to compare quantities as proportions of the whole set e.g.

• 5 out of 25 participants scored above 100 in a concentration task = 5:25

• 16 out of 100 participants stated that purple was their favourite colour = 16:100

As with fractions, a ratio should be reduced to its simplest form, e.g.

• 5:25 = 1:5

• 16:100 = 4:25

Significant figures are one way of dealing with very large (or very small) numbers

• A very large number can be rounded up to the nearest round number (a number that ends with a 0) e.g.

  • 596,321 would be rounded up to 600,000

  • 341,602 would be rounded down to 300,000

• For numbers with a decimal point, it is the digits after the decimal point that are rounded up or down e.g.

  • 0.00038967 to two significant figures is 0.00039 

  • 0.0000578 to two significant figures is 0.000058

Standard form is a way of dealing with very large (or very small) numbers without the process becoming too cumbersome and complex e.g.

• 10 to the power of 2 = 100 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 number)

Small numbers can also be written in standard form, however, the index (the ‘to the power of’ number) must be negative, e.g. 0.000000000000761 is written as 7.61 × 10^-13

You are expected to understand and use the following mathematical symbols

• equal to =

• less than <

• greater than >

• much less than<<

• much greater than >>

• proportional to ∝

• approximately equal ~