# Best approach to get a real value as average?

#### qualprod

Trusted Information Resource
Hi everybody

I come with question, hoping someone can give me some guidance.
This is may case.

Based under ISO , 9001, I´m starting to analyze data of production and want to
to get some values in average value.
In the case of analyzing days spent in production, I want to have a reference as a base, but
if I use an average value, it may result misleading.
this case, 10 work orders , one by one , days spent in production.
from 1 to 8 = 1 day, 1+1+1+1+1+1+1+1, but the 9 = 13 and 10 = 9
total sum of days is 30, divided by 10 = 3.
So average value for production is 3 days, which could be interpreted that sometimes
the work orders spend half a day, one day , while other times, 4 or 5 days.
But if we discard last two work orders (9 and 10), values could be = 1, which interpretation is very differente, we could say
Work orders spend half a day , while other times 1.5 days.
So in this case, which approach could be useful to adopt?
Please what is recommended, I don´t have statistical experience, so have no idea what to do.
what criteria to use, to get a values more closer to reality.

Thanks

#### Bev D

##### Heretical Statistician
Super Moderator
You have already realized that the average may be misleading. You are correct. It is misleading. So why keep trying? There is far more power in seeing the full variation of your data. Summary statistics can’t do that for you. As Deming cautioned us, summary statistics remove the most insightful aspects of data: the time series variation. The control chart is much more insightful. Just plot your data in time series order and forget about the average...

#### John Predmore

Trusted Information Resource
If there is a reason work orders 9 and 10 are not in a similar category as work orders 1 through 8, that would be a reason to exclude them from the average calculation, but that decision depends on what is the identified reason and what you want to communicate with your analysis. People here can not advise you what you want without knowing more about the situation and what you want to accomplish with your analysis. I agree with Bev D, it would be more meaningful to show the full picture with details on "outliers" so the recipients of the summary can judge what is meaningful to include and what makes sense to exclude.

#### Jim Wynne

I agree that the mean in many cases is misleading, and in some cases completely meaningless, depending on what you're trying to find out. There are two other measures of central tendency, however. In the case of your example data, the mode and the median value are both 1. Given the three numbers (mean, median, mode) you have a better picture of the makeup of the data. Additionally, you can calculate the range of the data, (the difference between the largest and smallest values) which will clarify further.

Nonetheless, plotting the data in time series as Bev suggests is the best way (again, depending on what you want to know).

#### qualprod

Trusted Information Resource
I agree that the mean in many cases is misleading, and in some cases completely meaningless, depending on what you're trying to find out. There are two other measures of central tendency, however. In the case of your example data, the mode and the median value are both 1. Given the three numbers (mean, median, mode) you have a better picture of the makeup of the data. Additionally, you can calculate the range of the data, (the difference between the largest and smallest values) which will clarify further.

Nonetheless, plotting the data in time series as Bev suggests is the best way (again, depending on what you want to know).
Thanks

There are two reasons, why I need these values

1- To have a reference to my customers, when they ask, what is your lead time for x product.
to give this information, what I did, was to measure spent time in work orders in a certain timeframe.
is a similar case to the one already given, I thought to give them average values, but if I get misleading
data, what can I give them as indicators of my productivity? (Lead time in days)

WO no.1 , took 1 day
#2, 1.5
#3, 3
#4, 2
#5, 1
#6, 2
#7, 1
#8, 2
#9, 13
#10,11
From 1 to 8, it was the normal/accustomed performance
In # 9, it was a special case, the raw material was imported and arrived very late, immediatelly started the production.
In # 10, It was a case where machinery failed, and spare parts also had problems, until problem was solved.
Both case were an anormal performance, from here, I can discard number 9 and 10, is it this way?, and get an average value
of the rest?

2- Other reason is to have data to be analized to develop improvements (to improve my production rate)
In this case, Ok, it sounds ok, not get an average, but analyze case by case and observer the complete performance,
This is what I catch.

#### Bev D

##### Heretical Statistician
Super Moderator
If your Customers are asking for lead times you should never use an average value. First of course is that approximately 50% of the time orders will exceed the average lead time. Lead time should be a promise that your planning group knows you can meet almost 100% of the time. It is not a statistical calculation...

As for improvement efforts, again the average doesn’t help. The control chart will...

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