Descriptive Statistics

Quick reference

• 00:04 Hi, I'm Ray Sheen, and it's time to lay a foundation,
• 00:08 for the Lean Six Sigma statistics.
• 00:11 Descriptive statistics will be the building blocks that we'll start with.
• 00:14 Statistics are a way to describe a dataset.
• 00:17 So let's start there.
• 00:19 A data set is a collection of data points associated with a problem or
• 00:23 process parameter.
• 00:24 With statistics, we can gain understanding about the data in the data set.
• 00:29 And we can make predictions about additional data that may be collected and
• 00:33 become part of that dataset.
• 00:35 Descriptive statistics summarize existing data with
• 00:38 the statistical terms like mean and standard deviation.
• 00:41 It provides insight about the collected data.
• 00:45 If that data set is only a subset of a total data population,
• 00:48 that descriptive statistics may be used to predict the performance of
• 00:53 the rest of the data in the population.
• 00:56 However, the key is this describes what exists in the data set.
• 01:02 Inferential statistics are a statistical analysis of the data to determine if
• 01:07 the data can support the inference associated with a hypothesis.
• 01:12 This will help us to draw conclusions about the real world that is reflected in
• 01:17 the data set.
• 01:18 And that means both the existing data and the dataset that we have and
• 01:22 potentially the full population of all the data that could be in the dataset.
• 01:27 Descriptive statistics can be used to predict the probability of an event that
• 01:31 is reflected within the dataset.
• 01:33 This provides insight about the characteristics that we would likely
• 01:37 observe and a sample of the data population.
• 01:41 Let's first describe the mean, median, and mode.
• 01:45 All three of these are statistics that tell us something about the central
• 01:49 tendency, or the most common value for the dataset.
• 01:53 First is the mean, or average value.
• 01:56 This is often referred to as an x with a bar over it and it's called, then, x bar.
• 02:03 The mean is very easy to calculate.
• 02:05 Just add all the data values together and then divide by the number of data points.
• 02:10 The mean is our favorite measure for central tendency when we have normal data.
• 02:14 And I'll talk more about that on another lesson.
• 02:17 One caution about the mean.
• 02:19 When there are large outliers in the data set,
• 02:21 that means a point that is extremely high or extremely low,
• 02:25 the mean can become significantly influenced by just a few key points.
• 02:30 Next is the median.
• 02:32 This is the middle point of the data set.
• 02:34 To find the median, you must first take the data set and order it from highest
• 02:39 to lowest, top to bottom, then, select the point that is in the middle.
• 02:45 If there are an odd number of points, the middle point is that median value.
• 02:50 If there are an even number of points, you have to select the two center values and
• 02:54 take the average of those two.
• 02:56 The median is used when we have a non-normal or skewed data set.
• 03:00 In that case,
• 03:01 it provides a better indication of central tendency than the mean.
• 03:06 The last measure is the mode.
• 03:08 This is the easiest to find since it is just the data value that
• 03:11 occurs most frequently.
• 03:14 While it's easy to find, it has very little value for us in Lean Six Sigma.
• 03:18 So let's shift gears now and consider the range, deviation,
• 03:22 standard deviation, and variance.
• 03:26 Whereas the mean value and median value were looking at central tendency of
• 03:30 the distribution, these statistics look at the edges of the distribution.
• 03:35 They tell us something about the span or
• 03:37 width of the data from the lowest to the highest value.
• 03:41 The first one of these is the range.
• 03:43 This is normally easy to determine.
• 03:46 Again, we order the data points from lowest to highest then we subtract
• 03:49 the value of the lowest from the value of the highest and you have the range.
• 03:53 It is the distance between the two extreme values.
• 03:58 Range is the distance between minimum to maximum.
• 04:01 Deviation is also a distance between two values.
• 04:05 However, in this case, it's a difference between the value of a data point and
• 04:09 the mean or average value of the data points in the set.
• 04:13 So deviation is always associated with a specific data point.
• 04:17 And it tells us how close that data point is at the center of the data.
• 04:23 If the deviation was 0,
• 04:24 it would indicate that that point is right smack in the middle of the data set.
• 04:30 Now, information about a single data point, while may be interesting for
• 04:35 that point, doesn't help us with respect to the data set.
• 04:39 So when we're looking at statistics,
• 04:41 we need to be able to describe the entire data set.
• 04:44 That is why we often use standard deviation in our statistical analysis.
• 04:48 The standard deviation provides a sense of the size of the expected data range.
• 04:54 This is calculated by taking each deviation, which I just described a moment
• 04:59 ago and squaring each of those, that means to multiply it by itself.
• 05:04 Add all those together, then divide by the number of data values.
• 05:08 Now finally, we take the square root of the result.
• 05:12 This is the standard deviation calculation,
• 05:15 and it is normally represented by the Greek symbol sigma.
• 05:19 The standard deviation is an excellent statistic for
• 05:23 estimating the normal range or span of data that will occur in the data set.
• 05:28 In fact,
• 05:29 the Six Sigma method derives its name from the standard deviation value, sigma.
• 05:35 The goal of Six Sigma was to create a process with a standard deviation that
• 05:40 was so small, that the range of -6 sigma to +6 sigma could fall within
• 05:45 the allowable tolerance limits for the process.
• 05:49 The variance will be the last of the descriptive statistic measures that
• 05:52 we'll discuss.
• 05:53 In fact, it's based on the standard deviation and
• 05:55 comes from squaring the standard deviation.
• 05:58 For some analysis,
• 05:59 the variance is much more important than the standard deviation itself.
• 06:03 These basic descriptive statistics will be referred to again and
• 06:08 again throughout this course and they will be covered exhaustively on the IASSC exam.

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