Describing Dispersion or Measuring Spread
This is a summary of lecture four of the Teaching Company course Meaning from Data: Statistics Made Clear. The course is very basic but it has helped to improve and revise my understanding of statistics. All I can recall from introductory statistics at university was confusion and anxiety.
In order to get meaning from a bunch of numbers we need to look at the traits that the data have. Below is a diagram I created to assist in my description.
The mean and median are measures of central tendency. The mean is the ‘balancing point’ around which all data sit. Outliers have a effect on that balance. The median is the mid point of the data points and is not affected by outliers. Neither gives us an indication of how spread out the data are.
A histogram gives us an visual approximation of the spread of the data. A five-number summary gives an simple numerical summary of the data from which spread can be deduced but does not allow us to visualise the overall shape of the data the way a histogram can.
Standard deviation and variance give a single digit summary of how varied the data are relative to the mean.
The next diagram gives a mechanical representation of the way the data is processed in order to produce the standard deviation.
The mean as well as each of the data points are fed into the equation in order to produce a single standard deviation value. The limitations that are associated with expressing data using the mean are incorporated into the standard deviation value, that is, it also is susceptible to outliers.
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- Data and Distributions
- Revising High School
- Continuing Basic Maths Revision
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