In this post, we discussed statistics as being made up of two branches - descriptive and inferential statistics. In today's post, we will be discussing what descriptive statistics entails. Tag along!
Descriptive statistics is a branch of statistics that that summarizes the information obtained from a sampled population. In other words, it deals with the summarizing of data obtained from a research with the description of basic features of the data. The summary of data are of two types:
Quantitative summary simply summarizes a large data into a single indicator. A good example is the student’s grade point average or the cumulative grade point average. It gives an indication of the overall performance of students from a list of courses the student must have taken. Another example is the percentage or frequency which indicates the proportion of a particular variate from a variable.
The visual summary gives a visual trend of a sample data at a glance. Examples include the bar chart, histogram, pie chart, line graphs, etc.
The distribution table is a summary of the number of times individual variates appear within a variable. A typical distribution table will contain a list of all the numbers within a single variable data set – usually in ascending or descending order - and the number of times they appear. More specifically, such table is referred to as the frequency distribution table.
To exemplify how a frequency distribution table is constructed, consider the following list of number of leaves found in 40 plants of the same species in a particular field:
06 10 05 09 05 09 09 10 08 09 09 09 05 08 05 09 08 09 07 08 07 09 06 08 09 07 08 08 09 05 08 08 06 07 05 06 10 08 06 07
At a glance, the data has no meaning until the variates are arranged in a form of table with their respective frequencies or any other descritptive statistical feature.
In order to construct a frequency distribution table for the data
The initial table looks like below
| Number of leaves | Frequency |
|---|---|
| 5 | 6 |
| 6 | 5 |
| 7 | 5 |
| 8 | 10 |
| 9 | 11 |
| 10 | 3 |
One can see that the table makes sense at a glance. Out of the 40 plants studied for their number of leaves, 6 had 5 leaves, 5 had 6 leaves, anothe 5 had 7 leaves, 10 had 8 leaves, 11 had 9 leaves, while only 3 plants had 10 leaves.
To further improve the distribution table and makes it more explanatory at a glance, a column of percentage can be added. The percentage of number of plants relative to the number of leaves they posses can be claculated such that:
percentage of plants with x number of leaves = frequency/total frequency x 100%
For example, the percentage of the sampled plants with 5 leaves can be calculated as:
| Number of leaves | Frequency | Percentage |
|---|---|---|
| 5 | 6 | 15 |
| 6 | 5 | 12.5 |
| 7 | 5 | 12.5 |
| 8 | 10 | 25 |
| 9 | 11 | 27.5 |
| 10 | 3 | 7.5 |
The data of number of leaves on the 40 plants can also be represented visually using a bar chart, scattered plot, or even a pie chart. In order to present the data in a bar chart, choose a suitable scale to represent the frequencies on the Y-axis and a suitable width for the bars that will represent each number of leaves on the X-axis.Thereafter, plot the various number of leaves against their respective frequencies to arrive at the figure below.
In order to present the data in a pie chart, each of the percentage or frequency is converted into an angle out of the total angle in a circle, which is 360O. For example, 6 plants had 5 leaves, the angle it will form within the pie chart would be;
6/40 x 360 = 54O
Once the angle each frequecy represents is calculated, the pie chart can then be drawn to scale using relevant instruments.
