Descriptive Statistics

Quick reference

• 00:05 Hi, I'm Ray Sheen and it's time to lay a foundation for
• 00:08 the Lean Six Sigma Statistics.
• 00:11 Descriptive Statistics will be the building blocks that we'll start with.
• 00:15 Statistics are a way to describe a data set.
• 00:19 So, lets start there.
• 00:21 A data set is a collection of data points associated with a problem or
• 00:24 process parameter.
• 00:26 While one data point is interesting, a data set which is made up of many data points
• 00:30 would provide a better description of that process parameter.
• 00:34 In fact the more data points you have, the more complete the picture.
• 00:38 When working with variable data, there are some data set characteristics
• 00:42 that can accurately describe that process parameter.
• 00:46 Those characteristics are mean, median,
• 00:48 mode, range, deviation and standard deviation.
• 00:53 Many times the data set will be a combination of variable and
• 00:56 attribute data.
• 00:57 So for instance in this table we have the attribute data element of a region, East,
• 01:02 North and West, or the reason for the service outage.
• 01:05 But then we have the variable data element of how much time until service was restored
• 01:11 and how many customers were affected.
• 01:14 Let's first discuss mean, median and mode.
• 01:17 All three of these are statistics that tell us something about the central
• 01:20 tendency or the most common value for the data set.
• 01:24 First is the mean or average value.
• 01:27 This is often represented by an x with a bar over it and called xbar.
• 01:32 The mean is very easy to calculate.
• 01:34 Just add all the data values and divide that sum by the number of data points.
• 01:39 The mean is our favorite measure when we have normal data.
• 01:41 And I'll talk about that more in other sessions.
• 01:45 One caution with the mean.
• 01:46 When there are large outliers in the data set, and
• 01:49 that means a point which is extremely high or extremely low.
• 01:53 The mean can be significantly influenced by those few points.
• 01:58 Next is the median.
• 01:59 This is the middle point in the dataset.
• 02:01 To find the median, you must first take all the values in your dataset and
• 02:06 put them in order by size from the smallest to the largest.
• 02:10 Then, if there are odd number of points, the middle point is the median.
• 02:14 If there are an even number of points,
• 02:16 the median is the average of the two center values.
• 02:20 The median is used when we have non-normal or skewed data since it provides
• 02:25 a better indication of central tendency than the mean does in that case.
• 02:31 The last measure is the mode.
• 02:33 This is easiest one to find since it is just the data value that occurs
• 02:37 most frequently.
• 02:38 While easy to find, this value is seldom used with Lean Six Sigma statistics.
• 02:44 So let's shift gears and now consider range deviation and standard deviation.
• 02:49 Whereas the mean and median were looking at the center of the distribution,
• 02:52 these statistics look at the edges of the distribution.
• 02:55 They will tell us something about the span, or
• 02:57 the width of the data from lowest to highest.
• 03:01 The first one is the range.
• 03:03 This is normally easy to determine.
• 03:05 Again, we ordered data points in the data set, from lowest to highest.
• 03:09 Subtract the value of the lowest from the highest, and you have the range.
• 03:13 It is the distance between the two extreme values in the data set.
• 03:18 Range is the distance from minimum to maximum.
• 03:21 Deviation is also the distance between two values.
• 03:25 However, in this case it is the difference between the value of a data point and
• 03:29 the mean or average of all the data points in the data set.
• 03:33 So deviation is always associated with a specific data point.
• 03:38 And it tells us how close that point is to the center of the data.
• 03:42 If the deviation was zero,
• 03:43 it would mean that data point was exactly equal to the mean of the data set.
• 03:48 No information about a single data point is interesting.
• 03:51 What we really want to have a statistic that describes the entire data set.
• 03:55 And that is why we often use the standard deviation in our statistical analysis.
• 04:00 The standard deviation provides a sense of the size of the expected data range.
• 04:06 This is calculated by taking each deviation,
• 04:09 which I just discussed a moment ago, and squaring each of them.
• 04:12 That means to multiply the deviation by itself.
• 04:15 Then add all of those deviation squared and divide by the number of data points.
• 04:21 Now finally, we take the square root of the result of that division.
• 04:26 This is the standard deviation calculation and
• 04:29 it's normally represented by the Greek symbol, sigma.
• 04:32 A standard deviation is an excellent statistic for
• 04:36 estimating the normal range or span of data that will occur for a data set.
• 04:41 In fact, the six sigma methodology derived its name
• 04:44 from the standard deviation sigma.
• 04:46 The goal of six sigma was to create a process with a standard deviation
• 04:51 that was so small, that a range of -6 sigma to + 6 sigma could fit
• 04:56 within the allowable tolerance limits for the process.
• 05:02 These basic descriptive statistics will be referred to again and
• 05:06 again throughout this course.
• 05:08 And they will be covered exhaustively on the IASSC exam.

Lesson notes are only available for subscribers.