# Measures of central tendency

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- This topic has 11 replies, 8 voices, and was last updated 12 years, 9 months ago by Mike Carnell.

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- May 26, 2007 at 9:46 pm #47093
How is central tendency meansured from a bimodial distribution?

0May 27, 2007 at 1:51 pm #156621This 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.0May 27, 2007 at 2:03 pm #156622A bimodal distribution has no central tendency.

0May 27, 2007 at 2:12 pm #156624

Mike CarnellParticipant@Mike-Carnell**Include @Mike-Carnell in your post and this person will**

be notified via email.Monica,

Mode is a measure of central tendency. Bimodal by definition has two.

Good luck0May 27, 2007 at 4:22 pm #156633Monica,

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.0May 27, 2007 at 4:28 pm #156634Twice.

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

0May 28, 2007 at 12:11 am #156643

Mike CarnellParticipant@Mike-Carnell**Include @Mike-Carnell in your post and this person will**

be notified via email.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.htm0May 28, 2007 at 2:30 am #156645There 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

0.07181

0.19942

0.26593

0.22654

0.13845

0.06466

0.02397

0.00728

0.00189

0.000410

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 2.0May 28, 2007 at 2:36 am #156647My 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.0May 28, 2007 at 2:57 pm #156665Thanks 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?

0May 28, 2007 at 4:03 pm #156672

Fake Gary AlertParticipant@Fake-Gary-Alert**Include @Fake-Gary-Alert in your post and this person will**

be notified via email.The optimum condition for CT when mean=median=mode

0May 28, 2007 at 5:56 pm #156676

Mike CarnellParticipant@Mike-Carnell**Include @Mike-Carnell in your post and this person will**

be notified via email.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.

Regards0 - AuthorPosts

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