# Average of Median?

Six Sigma – iSixSigma Forums Old Forums General Average of Median?

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• #49822

UKSS
Member

Im doing a project on reducing the number of days sales are outstanding for a collections company. My project Y is the median/average of number of days outstanding for invoices. I think I should be using a median value as the data will be skewed towards 0 days and an average would hide this.
Any thoughts?

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#170930

Sridhar Sukumar
Member

You need check the data distribution before determining this. Days being a continuous data, try a normality test. If the distribution is normal them mean is a right measure of central tendency, else you may use median.

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#170931

UKSS
Member

Thanks. When I get the data, I will do that but I expect it to be non-normal.

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#170936

Mikel
Member

Median

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#170937

Iain Hastings
Participant

UKSS,
I would suggest that you first construct a histogram of the data and ask what the distribution shows – for example does it look to be a single distribution or is it bi-modal or multi-modal? If there are multiple distributions working together then it is probably a reasonable starting point to try to identify and break out the individual elements.
Assuming that it is a single distribution at work, a probability plot could be used to determine the type of distribution. if you have Minitab it is straightforward to construct probability plots for various distributions (other than normal). Without attempting to prejudice your thought process I would suggest that you check your data a against an exponential distribution. Assuming that the data has a good fit to a recognizable distribution it is probably reasonable to use the mean value.

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#170938

Mikel
Member

Don’t make the question harder than it is.This is a naturally bounded distribution that is skewed right. Median is the right answer

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#170941

Stevo
Member

If it was me, and not many people are.  I would use both.

For many of the statistical tests, most likely median is your answer.  However, the client is probably doing this project because he is losing money for every day something is outstanding.

Does he/she care about the median?  Yes.  But he/she really cares about the mean.  It is possible to lower the median and increase the mean.  That would not be good.

Stevo has spoken.

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#170943

Outlier, MDSB
Participant

Stevo said, “Does he/she care about the median?  Yes.  But he/she really cares about the mean.”
I’ll bet what the customer really REALLY cares about are all those points way beyond either the mean or the median. Or maybe we’re all wrong about what the customer wants…
We are of course just guessing what the customer cares about, so you should go ask him. Determine what the customer’s upper spec limit is for days outstanding, determine how well the current process meets that need and how stable it is, then decide the best course of action. Let the data and the customer help you determine the right set of tools.
I know I’m preaching to the choir here, but I think it’s funny when learned professionals ignore their training and jump right to the conclusion. I know I’m guilty of it, probably more than I’d like to admit.
O.

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#170944

Gastala
Participant

It is possible that the time is related to the size (value) of the debt.
So you might want to plot these variables against each other initially, then stratify the data.
There may be different root causes associated with different subsets.
There may be one subset that gives the biggest hit.
Nothing profound here but hopefully it helps

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#170947

AJ
Participant

I agree with Stan that this dataset will be skewed right so you should use median as a measure of central tendancy, however, I also agree with Outlier in that since time is money, every day outside of the customer spec limit is a loss in opportunity, therefore, I would redefine the project Y as invoices outstanding past due date of 30, 60 or whatever the terms of the invoices are.  Then the goal statement may be “reduce overdue invoice span from x to hopefully 0”.  Span may be defined as the max minus the min of the 95% Confidence Interval of the overdue distribution.

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#170949

UKSS
Member

All valid points, and I have done the following.
We already have the customers ‘spec’ ie, they give us their target days sales outstanding. So, a defect is effectively any invoice that is paid after the target dso.
I am going to keep the project Y as median number of days invoices are overdue but use the percentage of customers whose dso is over their target dso as a secondary metric. Thoughts? (I know that matching the process to the customer specifications should be the project Y but it would require a significant change in the process to achieve this.)
I will look at both the mean and median, but like I said I expect the data to be way skewed to the right.

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#170983

Outlier, MDSB
Participant

UKSS,
Thanks for the clarification on what your customer expects. That adds a lot to the conversation.
I would talk to the customer with the approach that no process is perfect and there are bound to be occasional delays, what is the maximum percentage late they would be willing to live with? Say that it is 3% late (97% on time), then measure the current on-time delivery of the process and go from there.
I have seen this a lot in contract language with suppliers at my company where the metric is written, “4 hour average response rate” when what we, the customer really want is, “No more than 4 hour response rate.”  The supplier can average 4 hours as their response rate and comply perfectly with the metric, but in reality what it means is that about half of their calls take longer than 4 hours! To the customer it looks like a complete disaster.
Measure the way your customer measures. You can probably still get a lot of data from the process about median days overdue etc that will give you a very good understanding about the process and how it behaves. But make sure the customer can feel the improvements that you eventually make and can see them in a metric that makes sense to them.

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#170984

walden
Participant

Since this is a naturally positively skewed distribution, there is more more opportunity for improvement using the median. You may only have 10% of your data below the mean, but at the same time you’ll always have 50% of the data below the median. It is also easier to monitor the true level of the improvement using the median.

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#170999

UKSS
Member

Thanks Outlier.
Whilst I take your point in regards to aligning the project Y to our customers expectations and I agree that it is the idea measure, it is not feasible to use it as my primary metric for this project as we have over 128,000 customers all with varied target dso and limited management information and systems that allow us pro-actively collect based on target dso.
By reducing the median I will be able to decrease the pain for some customers. I will use the span as a measure and look at getting some VOC data on maximum dso to use that as a metric too.

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#171273

Saherngu
Participant

Two thoughts…………..It is what it is and, if the mean distribution is skewed, consider using a trimmed mean.

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#171283

Tex
Member

Not sure DSO is the proper measurment at the customer level. (DSO = Ending AR Balance / Credit Sales * Days in Period) and is generally used to measure the overall recievable process. May want to look at Average Days to Pay (or Median) for the overall process and then ADP for individual customers to drill down to the worst offenders. While ADP can be related to DSO it is not always related.

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