The Descriptive Statistics
Descriptive statistics is the branch of statistics that is responsible for collecting, organising, summarising, and presenting data in an understandable way, without drawing conclusions beyond the observed data.
It is used to describe and analyse a dataset through tables, charts, and statistical measures.
Main elements of descriptive statistics
Measures of central tendency (indicate the “typical” value of a dataset):
- Mean (
)
→ Average of values. - Median (Me) → Central value of the ordered data.
- Mode → Value that occurs most frequently.
Measures of dispersion (indicate how the data are spread out):
- Range → Difference between the maximum and the minimum.
- Variance (
) → Measure of the variability of the data. - Standard deviation (s) → Square root of the variance.
- Coefficient of variation → Expresses dispersion as a percentage.
Graphical representations (to visualise data clearly):
- Bar charts → For qualitative or discrete variables.
- Histograms → For continuous quantitative variables.
- Pie charts → For percentages and proportions.
- Boxplot (box diagram) → Shows dispersion and possible outliers.
Practical example
If we have a dataset with the response times of a server:
{4,0,0,3,33,,1,3,1}
Descriptive statistics allow us to:
- Calculate the mean: 1.88 seconds.
- Calculate the standard deviation: 1.55
- Build a histogram to see the distribution of response times.
Difference with Inferential Statistics
- Descriptive statistics → Summary and analysis of the observed data.
- Inferential statistics → Makes predictions or generalisations about a population based on a sample.
In summary, descriptive statistics help us understand and summarise a dataset without drawing conclusions beyond it.
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