AdvancedTopic 84 of 104Engineering Mathematics
Descriptive statistics
Mean, median, standard deviation and percentiles summarise datasets.
In depth
Descriptive statistics summarise data: mean, median, mode for centre; range, variance, standard deviation and interquartile range for spread; skewness for asymmetry. Histograms and box plots visualise them. The median resists outliers.
Key points
- Sample variance divides by n-1
- Percentiles describe distribution position
- Always plot data first
ExampleResponse times with a few extreme outliers have a mean much larger than the median.
What is Descriptive statistics?
Mean, median, standard deviation and percentiles summarise datasets.
Why is it important to understand descriptive statistics?
Descriptive statistics summarise data so you can compare batches, spot outliers and report results clearly.
When should I use the median instead of the mean?
Use the median for skewed data or data with outliers, because it is not pulled by extreme values.
What does standard deviation mean in plain words?
It is a typical distance of values from the mean, in the same units as the data.
How is Descriptive statistics used in practice?
Typical applications include reporting the average and spread of a set of tensile tests, finding the median response time of a web service and describing the typical energy use of a set of buildings.
What should I learn before Descriptive statistics?
Study "Central limit theorem" first (topic 83 of 104 in Engineering Mathematics). It covers the groundwork this topic builds on.
What are the key points of Descriptive statistics?
Sample variance divides by n-1. Percentiles describe distribution position. Always plot data first.
Can you give an example of Descriptive statistics?
Response times with a few extreme outliers have a mean much larger than the median.
What comes after Descriptive statistics?
The next topic is "Confidence intervals", which builds directly on this one.
How difficult is Descriptive statistics?
It is classed as Advanced in Engineering Mathematics (topic 84 of 104). It is an advanced topic. It assumes you are comfortable with the intermediate topics in Engineering Mathematics.