Six Sigma

Descriptive Statistics – Part 2

By Ron Pereira Updated on January 13th, 2011

Last night in part 1 of this series we began our discussion of descriptive statistics by introducing the three measures of central tendency – the mean, median, and mode.  As promised tonight we switch gears and are all about variation.

Customers Feel Variation

Like him or not Jack Welch made an impact on the business world.  One of the things he said in an annual report was that GE was great at “moving the mean” but not so good at battling the “variation” in the process.  Now I am paraphrasing here but that was the gist of his comment. 

This problem is so true in many organizations… many of us are all about moving the mean while the variation in the process continues to eat our lunch.

The Range

With this said, let’s begin our discussion of the three main measures of dispersion or variation with the range.  Many times we note the range of a data set the same time we note the median.  As mentioned last night, this is normally done when we are dealing with non normal data. 

To calculate the range we simply find the largest number in the data set and subtract from it from the smallest value in the data set.  Using the same example from last night {22, 11, 9, 9, 6, 2, 1, 1, 1} our range would be 21 (22 – 1).

The Variance and Standard Deviation

When dealing with normal, or so-called parametric data, the most popular measures of dispersion are the variance and standard deviation. 

Rather than bore you with the formulas for these two measures let me just say we first calculate the variance.  Then, once we know the variance we simply take the square root of the variance which gives us the standard deviation.  Of course with computers we can get straight to the standard deviation with the click of a few buttons (as we will show below). 

If you are terribly bothered by not knowing the formula for the standard deviation click on the picture above and study it to your hearts desire.

In most cases we will note the standard deviation along with the mean.  So it may sound something like this:  Our process averages 25 with a standard deviation of 3.

MS Excel Tips

MS Excel can once again help us calculate these measures of dispersion. Here’s how to do it:

  1. For the range use the following: =max(data set)-min(data set)
  2. For the variance use the following: =var(data set)
  3. For the standard deviation use the following: =stdev(data set)

Sample and Population Statistics

There is one more topic I intend to touch on in a later post related to the difference between “sample” statistics and “population” statistics which basically has to do with how accessible data is. 

If, like in most cases, you are not able to collect all the data that ever was and ever will be we will almost always rely on sample statistics.  But let’s save this groovy discussion for another night.

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  1. Rob

    August 22, 2007 - 5:36 am

    I really like the phase you use here Ron: Customers Feel Variation.

    When asked what I do for a living I always reply in two words: minimize variation. Is this the shortest job description in the world?


  2. S

    August 22, 2007 - 6:35 pm

    More I say! These last 2 articles on stats have been great. I’m normally not a stats fan but I’ve enjoyed these articles and would love to hear more

  3. Ron Pereira

    August 22, 2007 - 8:11 pm

    Thanks S. I will say your comment gave me a serious scare. I have a plugin that sends an email to new commenters and since you used S for the email it caused the plugin to flip out and I couldn’t even access the site. Luckily my hosting company could go in the back way and delete the plugin! No sweat… that plugin was over rated anyhow.

  4. Muhammad Rafi

    August 23, 2008 - 10:56 pm

    Asslam-o-Alaikm(May Allah bless you with peace and mercy)
    you must add numerical example which define the conceptual use of these measures.

  5. don

    October 2, 2008 - 4:59 pm

    this does not tell me how to calculate standard deviation or variance. maybe cause I’m a laymen

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