I want to know why Mean is preferred over median in control charts. What is the criteria used in deciding Mean or median?

I want to know why Mean is preferred over median in control charts. What is the criteria used in deciding Mean or median?

Hello bkarthikeyan,

Here's a start:

http://www.nwea.org/support/kb/issue_view.asp?ID=265&CATE=19

http://standards.nctm.org/document/eexamples/chap6/6.6/index.htm

http://regentsprep.org/Regents/math/ALGEBRA/AD2/measure.htm

http://www.anu.edu.au/nceph/surfstat/surfstat-home/1-2-2.html

http://www.maths.murdoch.edu.au/units/statsnotes/samplestats/medianmore.html

I will further investigate....

Stijloor.

Brief summary:

Medians are less sensitive to extreme scores and are probably a better indicator generally of where the middle of the class is achieving, especially for smaller sample sizes. Means are the arithmetic average and are often used with larger sample sizes.

Mean (http://elsmar.com/wiki/index.php/Mean) and Median (http://elsmar.com/wiki/index.php/Median) are two types of "averages" or measures of central tendency. Both measures appear in everyday media reports, and they are generally studied by students in the elementary and middle grades. The median is a measure of the "middle" of the data. For an odd number of data points arranged in ascending order, the median is actually the middle value, and for an even number of data points it is the value halfway between the two middle data points. The mean (a number which "evens out" or balances a set of data) is computed by adding all the numbers in the set and dividing the sum by the number of elements added. For a given set of data, these measures of center may be very close or may be quite different, depending on how the data are distributed, and either of the measures of center may or may not provide a good measure of "typicalness."

The mean and median each have advantages and disadvantages when used to describe data sets. The mean depends on the actual values in a data set, but the median is dependent only on the relative position of the values. Changing one data value does not affect the median, unless the data value is moved across the middle of the data set. But every change in a data value affects the mean. Thus, the mean is affected by a few extremely large or extremely small values outside the range of the rest of the data, but the median is not.

How do I know which measure of central tendency to use?

Use the mean (http://elsmar.com/wiki/index.php/Mean) to describe the middle of a set of data that does not have an outlier.
Advantages:
• Most popular measure in fields such as business, engineering and computer science.
• It is unique - there is only one answer.
• Useful when comparing sets of data.
Disadvantages:
• Affected by extreme values (outliers)

Use the median (http://elsmar.com/wiki/index.php/Median) to describe the middle of a set of data that does have an outlier.
Advantages:
• Extreme values (outliers) do not affect the median as strongly as they do the mean.
• Useful when comparing sets of data.
• It is unique - there is only one answer.
Disadvantages:
• Not as popular as mean.

My! Excellent answer Marc! Are you writing a book or something?

http://elsmar.com/jpg/Einstein_Head.jpg

All I was going to add is if you assume a normal distribution with a control chart (which many don't), the mean and median are the same.

No book - Just adding content.

Are you going to put that one in Wiki under median and mean?

Davis Ballestracci (was head of the ASQ Stats Division a few years back) is a big proponent of using the median. He's written a couple of books on the subject.

In Shewhart's Economic Control of Quality of Manufactured Product, there is a comparison of using the median and the mean for the center line of a control chart. Shewhart made the decision to go to the mean because it converges on the central characteristic of a sample of the data faster than the median does.

Add to Marc's remarcs on median Disadvantages:
• More difficult to calculate, the way to calculate the median is ordering the data and take the value on the middle of the array (without Excel/Lotus spreadsheets you may need a sorting function).

Maybe also a point in Shewhart desicion to use mean.:confused:

:topic: Are you going to put that one in Wiki under median and mean?
A bit of it.

One of the benefits of the median is that it can simplify calculations on the shop floor for lesser skilled operators. A three point sample is taken. The lowest of the three is subtracted from the highest of the three and that is the range. The one you did not use is the median. No adding, no dividing. Very fast for those who have time issues.

But, of course, neither mean or median is correct for precision machining.:cool:

But, of course, neither mean or median is correct for precision machining.:cool:

What is your sugestion if mean nor median are good estimates?, geometric mean? :confused:

What is your sugestion if mean nor median are good estimates?, geometric mean? :confused:

The mean (or median and mode) has no real point in controlling the uniform distribution. The only thing that counts is the control limits. The best chart is the X hi/lo-R chart for precision machining. It will not only control the process correctly, without overcontrol, but it will also allow you to calculate tool wear much more precisely. Correct control and more information on the process? Who can ask for more than that? :cool:

See: http://elsmar.com/Forums/showthread.php?t=20935 for details.

I want to know why Mean is preferred over median in control charts. What is the criteria used in deciding Mean or median?

Wheeler gives a very detailed analysis of this and comparison with other measures, in Chapter 3 "Advanced Topics in SPC".