Paolo Gironi - notes on data analysis, SEO, statistics and retro computing

The Normal Distribution, the Z-Score and the Z-Table

The concept of the normal distribution is one of the key elements in the field of statistical research. Very often, the data we collect shows typical characteristics, so typical that the resulting distribution is simply called… “normal”. In this post, we will look at the characteristics of this distribution, as well as touch on some other concepts of notable importance such as:

the empirical rule
the standardized variable – The concept of Z score
Chebyshev’s inequality

Mean, median or mode? Which measure of position to use (and when to get it wrong)

Two weeks of organic sessions, a Black Friday in the middle, and the report says: «385 sessions a day, on average». Except that no normal day came anywhere near it: the typical day had 233.
It is not a calculation error (the mean is right), it is the wrong measure for those data. Choosing the number that sums up a distribution is the first move of any analysis, and also the first way to be fooled.

Measures of position (or measures of central tendency) are there for exactly this: telling us, with a single value, where the data concentrate. Let’s look at the various means, the median, the mode, quartiles and percentiles, when to use which, and how to compute them in R in a moment.