2022 Introduction to Statistics in Research Mitchell 2nd ed

I N T R O T O R E S E A R C H : D A T A V I S U A L I Z A T I O N & C O M M O N S T A T T E S T S

Normal Distribution Review A normal distribution, called the "bell curve" or Gaussian Distribution, is a continuous probability distribution that is symmetrical. This is the standard comparison for describing distributions of sample data. Let's look at the illustration below that was built in Statistics Kingdom. The empirical rule in statistics allows you to determine the proportion of values that fall within certain distances of the mean. Note that in a normal distribution, the mean will be equal to both the median and the mode!

Table 70: Normal Distribution Showing Empirical rule

Notice that at one standard deviation from the mean (-1, or 1), expect 68.2% of the values to fall under this section of the distribution. So if these were scores, you would have a 68% chance of selecting a score between -1 and +1 standard deviations from the mean. The normal distribution is one of the most important statistical concepts in Lean Six Sigma. In fact, the "six sigma" is directly related to the six standard deviations (3 negative and 3 positive) in a normal distribution. Six sigma has come to mean a quality management process, and some of you will (or already have) earn a yellow, green, or black belt certification.

Kurtosis: The new definition of kurtosis measures "tailedness" rather than "peakedness", but you can see the difference in the images shown here. I apologize for my simple drawings!

Mesokurtic Curve

Leptokurtic Curve

Platykurtic Curve

To understand more about Shapes of Distributions, please feel free to watch Kahn Academy. But for now, it is enough to know that not all data will graph the same.

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