Numeracy, Maths and Statistics - Academic Skills Kit

Ratios (Psychology)

ContentsToggle Main Menu 1 Introduction 2 Worked Example 3 Test Yourself 4 External Resources

Introduction

A ratio is the proportional relationship between two or more different quantities. A ratio is usually displayed using a colon ' : '.

Here is an example showing how ratios work. In a university, the ratio of professors to lecturers to students is $1:5:20$ . This means for every $1$ professor there are $5$ lecturers and $20$ students.

If you want to convert ratios into fractions the following formula will help:

$\begin{equation} \text{To convert the ratio A : B : C into fractions:} \frac{\text{A}}{\text{(A + B + C)}} , \frac{\text{B}}{\text{(A + B + C)}} , \frac {\text{C}}{\text{(A + B + C)}}. \end{equation}$

Worked Example

You work as a psychologist. You often need to write prescriptions for patients. For patients with depression you administer Fluoxetine at a dose rate of $21$ mg for every $60$ kg of body weight per day. For patients with anxiety you administer Paroxetine at a dose rate of $15$ mg for every $50$ kg of body weight per day.

You have a patient who you have diagnosed with depression and anxiety. He weighs $91$ kg; how much medication should you prescribe for a week?

Solution

Firstly, calculate how much of each drug he needs per day:

For Fluoxetine: he needs a dose rate of $21$ mg per $60$ kg and he weighs $91$ kg. The method for calculating this is to divide $21$ mg by $60$ to find out the dose rate per kg and then multiply this by $91$ to give:

$(21 \div 60) \times 91 = 31.85$ mg of Fluoxetine per day.

For Paroxetine: he needs a dose rate of $15$ mg per $50$ kg and he weighs $91$ kg. Divide $15$ mg by $50$ to find the dose rate per kg and multiply by $91$ to give:

$(15\div 50) \times 91 = 27.3$ mg of Paroxetine per day.

So per week you need to perscribe $31.85 \times 7 = 222.95$ mg of Flouxetine and $27.3 \times 7 =191.10$ mg of Paroxetine to your patient.

Test Yourself

Try our Numbas tests on background mathematics.

External Resources

Ratios from Maths is Fun