Normal Distribution

All posts tagged Normal Distribution

Statistics is the study of the collection, organization, analysis, interpretation and presentation of data (wikipedia). To this end some averages (the middle) and standard deviations (the variation from the middle) are some of the basic calculations in statistics which we use every day. The average of three numbers can be calculated by adding them all together and dividing by the number of numbers there are. For example in the following sequence: 1, 2, 3 there are three numbers (we write this as “n=3”). The average can be calculated by adding them together: 1+2+3 = 6 and dividing this total by the number of numbers to calculate the average: 6/3=2. The average of 1, 2, 3 is 2. The “average” can also be called the “mean”. Both words describe the same thing. Symbol wise we can also call the “average” or “mean” x-bar and write it as an “x” with a line over as in: xbarSo the Average = Ave = Mean = xbar

The standard deviation is the difference between the x̄ and the other numbers in the sequence. we usually calculate standard deviation using calculators or excel but it can be easy to work out for some sequences. So back to the sequence 1, 2, 3 where the x̄ was 2 the standard deviation is 1 because x̄ + 1 is 3 (the upper number in our sequence) and x̄ – 1 is 1 the lower number in our sequence. Symbol wise we can also write the “standard deviation” as a p on it’s side: σ

So the Standard Deviation = StDev = σ

When we display data in figures to assess it’s quality we will often use histograms. These figures consist of an “x” and “y” axis. The x being the horizontal axis and the y being the vertical axis. Each axis is used to display data of some sort such as sample weight on the “x” axis and the number of samples of a particular weight on the “y” axis (also known as the frequency). If we re order the collected data on sample weights such that samples with the smallest weights are to the left of the “x” axis and the samples with the highest weights are to the right of the “x” axis we can in most cases produce a a bell shaped histogram such as the one below.


This is known as a “bell shaped curve” or “normal distribution” or a “Gaussian curve”.