A Beginners Guide to Statistics Equations

For those who think statistics notation is just hieroglyphics for nerds—this blog’s for you!

In a Lean Six Sigma Course you will be introduced to concepts such as mean, median, variance, standard deviation and probability, even worse than this! we will show you the equations and how to use them. Most of you will have been through this education before (I’m talking in High School) and most of you will have forgotten this, or blocked the memory away like a cat burying its business in the litter box.

In this blog I am going to help you understand some of the squiggly symbols Master Black Belts like to put in front of you when we introduce Green Belts and Black belts to some the statistics used in Lean Six Sigma Education.

Compact Descriptive Formulas

There are different ways to write mathematical formula, in this blog we will be using the ‘Compact Descriptive’ style. This means that in other publications you may well see some of the equations below written differently to how I show them below. Don’t worry, just all equations can be understood if you break them down into their component parts.

I have trained many people in Lean Six Sigma and the fun (confusion and sometimes fear) normally starts when explaining the Sigma part of Lean Six Sigma. We have to go into the world of maths and statistics because Sigma (σ) is standard deviation

σ = \sqrt{\frac{\sum (x_i - \bar{x})^2}{N}}

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I plan to do a separate blog just about this subject, but for now just think of it as a score as to “How much things vary”, the bigger the number the more they vary.

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I am going to make an assumption that you are OK with some of the symbols such as: Equals $=$ , Squared $^2$ , plus $+$ , minus $-$ divide / , multiply $×$ and square root $\sqrt{}$ ( yes I know, assumptions are dangerous! )

Lets start with something easy!

the symbol Σ is the upper case version of the Greek letter sigma, and in maths it is used to represent the sum of a sequence of numbers

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σ is the lower case of the Greek letter sigma, it is also used in statistics equations. It is used to represent the Standard Deviation of a Population of data

$Σ$ tells us to sum something, in this case its going to be what’s inside the brackets. $x_i$ is used to represent data, because we are writing a formula that can be used for any set of numbers, $x_i$ represents all the numbers in the set. the $i$ standards for individual.

Example: lets say we have a set of numbers 1, 2, 3. $\sum x_i = \sum(1,2,3) = 1+2 +3 = 6$

$\bar x$ (x bar) represents the MEAN of a data set, Its a symbol everyone involved in Lean Six Sigma should understand!

$\frac{\sum x_i}{N}$ is the formula for the MEAN of a population of data

BIDMAS - The Route to Solving Maths Equations

Before we start looking at some of the other symbols within maths equations, let me introduce to BIDMAS is an acronym that helps you remember the order of operations in mathematics. It’s a modern teaching shortcut for rules established by mathematicians over hundreds of years! It stands for:

Brackets: Solve anything inside brackets first.
Indices: Work out powers (e.g., $222^2$ ) and roots (e.g., $4\sqrt{4}$ ).
Division: Solve from left to right.
Multiplication: Solve from left to right.
Addition: Solve from left to right.
Subtraction: Solve from left to right.

For example when solving the equation: $2+3×(4−1)^2$

Brackets: $(4−1)=3$
Indices: $3^2=9$
Multiplication: $3×9=27$
Addition: $2+27=29.$

Answer is 29

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Following BIDMAS ensures calculations are done in the correct order to get the right answer.

More to come soon 😊