CALCULATION OF PERCENTAGES

Providing percentages in a dataset summary can help the reader get a feel for the data at a glance without needing to read all the results. For example, if two conditions compare the effects of revision vs no revision on test scores, a psychologist could report the percentage of participants who performed better after revising to provide a rough idea of the study's findings. Let’s imagine that out of 45 participants, 37 improved their scores by revising.

To calculate a percentage, the following calculation would be used:

Number of participants who improved × 100 Total number of participants

The bottom number in the formula should always be the total number in question (such as the total number of participants or the total possible score), with the top number being the number that meets the specific criteria (such as participants who improved or a particular score achieved). This answer is then multiplied by 100 to provide the percentage.

CALCULATION OF PERCENTAGE INCREASE

First, the difference between the two numbers being compared must be calculated to determine the percentage increase. Then, the increase should be divided by the original figure and multiplied by 100 (see example calculation below).

For example, A researcher was interested in investigating the effect of listening to music on the time to read a text passage. When participants were asked to read with music playing in the background, the average time to complete the activity was 90 seconds. When participants undertook the activity without music, the average time to complete the reading was 68 seconds.

Calculate the percentage increase in the average (mean) time to read a text passage when listening to music. Show your calculations. (4 marks)

Increase = new number – original number Increase = 90 – 68 = 22
% increase = increase ÷ original number × 100 % increase = 22 ÷ 68 × 100
22/78 = 0.3235
0.3235 × 100 = 32.35%

CALCULATION OF PERCENTAGE DECREASE

First, the difference between the two numbers must be calculated to determine the percentage decrease. Then, the decrease should be divided by the original figure and multiplied by 100 (see example calculation below).

For example, a researcher was interested in investigating the effect of chewing gum on the time it takes to tie shoelaces. When participants were asked to tie a pair of shoelaces in trainers whilst chewing gum, the average time to complete the task was 20 seconds. When participants undertook the activity without chewing gum, the average time to tie the shoelaces was 17 seconds.

Calculate the percentage decrease in the average (mean) time taken to tie shoelaces when not chewing gum. Show your calculations. (4 marks)

Decrease = original number – new number Decrease = 20 – 17 = 3
% decrease = decrease ÷ original number × 100 % decrease = 3 ÷ 20 × 100
3/20 = 0.15
0.15 × 100 = 15%

POSSIBLE EXAMINATION QUESTIONS

Name one measure of central tendency. (1 mark)
Exam Hint: As this question asks for a measure of central tendency to be named, no further elaboration is required to gain the mark here.

1. Which of the following is a measure of dispersion? (1 mark)

   Mean

   Median

   Mode

   Range

2. Calculate the mode for the following data set: 10,2,7,6,9,10,11,13,12,6,28,10. (1 mark)

3. Calculate the mean from the following data set. Show your workings: 4, 2, 8, 10, 5, 9, 11, 15, 4, 16, 20 (2 marks)

4. Explain the meaning of standard deviation as a measure of dispersion. (2 marks)

5. Other than the mean, name one measure of central tendency and explain how you would apply this to a data set. (3 marks)

   Exam Hint: It is vitally important to take time to read the question fully to ensure that a description of how to calculate the mean is also provided.

6. Explain why the mode is sometimes a more appropriate measure of central tendency than the mean. (3 marks)

7. Explain one strength and one limitation of the range as a measure of dispersion. (4 marks)

8. Evaluate the use of the mean as a measure of central tendency. You may refer to strengths and limitations in your response. (4 marks)

9. A researcher was interested in investigating the number of minor errors made by male and female learner drivers on their driving tests. Ten males and ten females agreed to have their driving test performance submitted to the researchers. The table below depicts the findings: