# What is the correct way of describing this change - mean or median?

## Main Question or Discussion Point

Hi,

Please see the attached Excel file.

The list shows the old and new values of a set of variables. I am trying to understand what is the best way – average or median - to describe the change the values of the set. I want to describe the true central tendency of the change.

1. I think there are the following four ways I can describe the change in the values of the set . Which one is the most accurate?

a) the average value changed by 0.15% (the mean of the change values shown in Cell E63)
b) the average value changed by 0.10% (the median of the change values shown in Cell E64)
c) the average value changed by 0.14% (the difference of Cell D63 and C63)
d) the average value changed by 0.25% (the difference of Cell D64 and C64)

2. I am ignoring the change values of variables X12 and X39, as these variables did not change. Is that correct?

Thanks.

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mfb
Mentor
Certainly not the median of the differences (b).

Both distributions look nice, not too asymmetric and without outliers. I think I would compare the average values. a and c should give the same result here.

2. I am ignoring the change values of variables X12 and X39, as these variables did not change. Is that correct?
Don't ignore them, they are measured values! This could just be by chance, and also a result of your measurement resolution.

• 1 person
Certainly not the median of the differences (b).

Both distributions look nice, not too asymmetric and without outliers. I think I would compare the average values. a and c should give the same result here.
Can you explain why you think B should not be used? Is it because the distribution of change values is not symmetrical?

mfb
Mentor
I cannot imagine a scenario where the median of the differences would have an advantage over anything else, unless the correlation between your measurement series is much stronger than the correlation within the series (so you have something like 0.10 -> 0.11, 45343.44 -> 45343.45 and similar things, together with some outliers so the mean cannot be used). But then you should not compare the series like that anyway. I am not sure what you are saying here.

I prefer the median over the mean when there are outliers in the data.

I cannot imagine a scenario where the median of the differences would have an advantage over anything else, unless the correlation between your measurement series is much stronger than the correlation within the series (so you have something like 0.10 -> 0.11, 45343.44 -> 45343.45
Are you talking about auto-correlation here?
Also, I don't know what you mean by 'measurement series'.

mfb
Mentor
I prefer the median over the mean when there are outliers in the data.
Right.

Are you talking about auto-correlation here?
It is related to that.
Also, I don't know what you mean by 'measurement series'.