Analysing quantitative data
If you have collected quantitative data, you will have information relating to numbers which you can display and analyse using mathematical techniques.
Statistics help turn quantitative data into useful information. This can be done by using:
- frequency analysis
- percentage analysis
- centre and spread analysis
Frequency analysis
Frequency analysis deals with When data is grouped into categories.. This is when data can be grouped into different categories. For example, in a group of people there may be two categories – male and female. The number of females in the female category is the frequency.
Frequency tables can be used to present findings, or they can be converted into graphs or bar charts for a more visual representation.
A table or a bar chart could be used to represent the answers given by a class of 14-year-olds about their ideal job.
Table format
| Ideal job | Frequency |
| Teacher | 5 |
| Pilot | 2 |
| Model | 2 |
| Chef | 3 |
| Doctor | 6 |
| Nurse | 2 |
| Fashion Designer | 1 |
| Ideal job | Teacher |
|---|---|
| Frequency | 5 |
| Ideal job | Pilot |
|---|---|
| Frequency | 2 |
| Ideal job | Model |
|---|---|
| Frequency | 2 |
| Ideal job | Chef |
|---|---|
| Frequency | 3 |
| Ideal job | Doctor |
|---|---|
| Frequency | 6 |
| Ideal job | Nurse |
|---|---|
| Frequency | 2 |
| Ideal job | Fashion Designer |
|---|---|
| Frequency | 1 |
Bar chart format
Percentage analysis
The data from frequency tables can also be converted into percentages in order to make the data clearer using the following formula.
\({\percent}~{=}~\frac{Frequency}{Total}~{\times}~{100}\)
This table clearly shows that the most popular category was to become a doctor. But it also gives information about the relative frequency of each category. Relative frequency means you can compare one frequency to another, eg the choice of nurse is twice as popular as the choice of fashion designer.
| Ideal job | Frequency | Percentage |
| Teacher | 5 | 23.8% |
| Pilot | 2 | 9.5% |
| Model | 2 | 9.5% |
| Chef | 3 | 14.3% |
| Doctor | 6 | 28.5% |
| Nurse | 2 | 9.5% |
| Fashion Designer | 1 | 4.9% |
| TOTAL | 21 | 100% |
| Ideal job | Teacher |
|---|---|
| Frequency | 5 |
| Percentage | 23.8% |
| Ideal job | Pilot |
|---|---|
| Frequency | 2 |
| Percentage | 9.5% |
| Ideal job | Model |
|---|---|
| Frequency | 2 |
| Percentage | 9.5% |
| Ideal job | Chef |
|---|---|
| Frequency | 3 |
| Percentage | 14.3% |
| Ideal job | Doctor |
|---|---|
| Frequency | 6 |
| Percentage | 28.5% |
| Ideal job | Nurse |
|---|---|
| Frequency | 2 |
| Percentage | 9.5% |
| Ideal job | Fashion Designer |
|---|---|
| Frequency | 1 |
| Percentage | 4.9% |
| Ideal job | TOTAL |
|---|---|
| Frequency | 21 |
| Percentage | 100% |
Centre and spread analysis
The centre describes a typical value and the spread describes the distance of the data from the centre.
The most common statistics to describe a centre are:
- mean
- median
- mode
The mean is calculated by adding up all of the values (21) and dividing by the number of values (5, 2, 2, 3, 6, 2, 1 = 7 values). This makes the mean 21 ÷ 7 = 3.
The median is the middle value when all the values are placed in chronological order. This makes half the data set greater than the median, and half the data set smaller. In the example the halfway point is 2, ie 1,2,2, 2, 3,5,6.
The mode is the most popular occurrence of a value. In the example the most popular value is 2.
Spread is the range of the data. This is the difference between the minimum value and the maximum. In the example, the range is 5.
The greater the spread, the less likely it is that the median and mean will be good representatives of the original values. The smaller the spread, the more likely it is that the median and mean will be good representatives of the values in the original dataset.
