# 12.6.3  Proportion and percentage

A proportion, sometimes called relative frequency, is simply the number of times the observation occurs in the data, divided by the total number of responses. Proportions are very often converted to percentage values because this makes comparison easier between different sets of data. Percentage means the number of occurrences or responses, as a proportion of the whole, multiplied by 100. For example, if 30 people respond to a survey out of a total of 100, the frequency of respondents is 30, the proportion is 30/100 or 0.3, and the percentage of respondents is 30%. If the total number of people surveyed was only 60 and there were 30 respondents, the proportion is 30/60 or 0.5, and the percentage of respondents is 50%.

• Approximately what percentage of the seven people whose answers are summarised in Table 12.2 are illiterate?

• Three of the seven people are illiterate. So the percentage of people who are illiterate is 3/7 × 100% which is approximately 43%.

• Go back to Table 12.4b, which showed the number of people who have had malaria in different age categories, and add a column to show the percentage of each age category that have had malaria. Which age category has the highest percentage of people who have had malaria?

• Your table should look something like Table 12.5 below.

## Table 12.5  Age distribution of the number and percentage of people who have had malaria in an imaginary example.

Age group(years)Number of people sampledNumber who have had malariaPercentage who have had malaria
over 50252080%
30 to 50251976%
under 30251456%

To calculate the percentage, you take the number who have had malaria and divide it by the total number sampled, then multiply your answer by 100. For example, in Table 12.5, for those aged over 50 years, the calculation is 20 (who have had malaria), divided by 25 (people sampled) × 100%, which is 80%. This is the age group with the highest percentage of people who have had malaria.

Table 12.6 shows the percentage of women in each of four age groups in a certain population. It shows that more women fall in the age group 30–40 years than in any other category.

## Table 12.6  Percentage of females by age group.

Age groupNumber of womenPercentage of total
under 3020017
30–4040033
41–503529
over 5025021
all ages1200100

In the example in Table 12.5, only 25 people in each age group were sampled. When reporting percentages, you should also always report how many observations there were. For example, if you say that 50% of women seen by the clinic this month had diabetes, it is important to know how many women were seen. If it is 50% of 500 women, this means that 250 women with diabetes were seen, but if it is 50% of two women, then only one woman with diabetes was seen!

12.6.2  Mean, median and mode

12.6.4  Cumulative percentage