# Measures of central tendency

Six Sigma – iSixSigma Forums Old Forums General Measures of central tendency

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• #47093

G
Participant

How is central tendency meansured from a bimodial distribution?

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#156621

Rupesh
Member

This looks to be good question to me. The options I can think of,
1. Find out the favourable one from the two responses and do analysis for the favourable data. By favourable I mean if its a project related to yield, higher of the two means will be favourable. If its a cycle time project, lower of the two means will be favourable. Hence we need to identify factors for achieving the favourable response.
2. In my view the analysis should be done for recent data, that will be the true representative of the process.

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#156622

WMD
Member

A bimodal distribution has no central tendency.

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#156624

Mike Carnell
Participant

Monica,
Mode is a measure of central tendency. Bimodal by definition has two.
Good luck

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#156633

annon
Participant

Monica,
It generally isnt…once you determine your distribution type is bimodal, you have uncovered that you are working with two different sets of operating conditions….the goal then is to go back into the data and isolate the two.  Then you will use the CT that is appropriate for each based on their distribution type and your analytics.  GL.

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#156634

Craig
Participant

Twice.
Once for the left-most distribution, and once for the right-most distribution.

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#156643

Mike Carnell
Participant

Anon,
I am not sure when the mode stopped being a measure of central tendancy. Granted it may be two sets of operating conditions but that dat set, as presented, is bimodal and any other measure of central tendancy will be misleading.
https://www.isixsigma.com/dictionary/Central_Tendency-119.htm

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#156645

Doc
Participant

There is a lot of confusion about the binomial distribution in this thread.
The binomial distribution involves the random variable x, where x is number of “successes” from n trials where each trial involves a probability of success equal to p.
The potential values of x are 0, 1, …, n, and the binomial distribution gives the values for each of theses potential x-values.
The binomial distribution for n=10 and p-0.25 is:

0
0.0718

1
0.1994

2
0.2659

3
0.2265

4
0.1384

5
0.0646

6
0.0239

7
0.0072

8
0.0018

9
0.0004

10
0.0001
The expected value of x (or the mean) is equal to np. In this example that is 10(0.25)=2.5
The median is the value of x at which we find the 50th percentile. In this example that would be 2.
The mode is the value of x which has the highest probability of occurance, which in this example would be 2.

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#156647

Doc
Participant

My mistake. I thought the original post said “binomial” instead of “bimodial”.
For bimodal distribution most people would probably use the 50th percentile, though a better strategy would be to try to determine the cause of the two modes, isolate them, and then characterize each cause separately.

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#156665

annon
Participant

Thanks for the clarification mike…..didnt mean to suggest otherwise…my only advice was to determine the reason for the bimodality before moving forward with the analysis and descriptors…is this not a correct course of action?

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#156672

Participant

The  optimum  condition  for  CT when mean=median=mode

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#156676

Mike Carnell
Participant

annon,
No question on the course of action. I agree with you completely. It is actually avery nice situation to have because it makes it easier to decide where to go next.
Regards

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