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

• musicgold
In summary, the conversation revolves around finding the best way to describe the change in values of a set of variables. There are four possible options, with options a and c being the preferred methods. The use of the median (option b) is not recommended unless there are outliers in the data or a strong correlation between measurement series. Additionally, the change values of variables X12 and X39 should not be ignored when comparing the average values.

#### musicgold

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.

#### Attachments

• Mean vs Median.xlsx
20.9 KB · Views: 230
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
mfb said:
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?

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.

mfb said:
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'.

musicgold said:
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'.

## 1. What is the difference between mean and median?

The mean is the average of a set of numbers, calculated by summing all the numbers and dividing by the total number of values. The median is the middle value of a set of numbers when they are arranged in order from smallest to largest.

## 2. When should I use the mean to describe a change?

The mean is most useful when the data is normally distributed and there are no outliers. It gives a good representation of the central tendency of the data.

## 3. When is the median a better measure of change?

The median is a better measure of change when the data is skewed or there are outliers. It is less affected by extreme values and gives a more accurate representation of the typical value in the data set.

## 4. Can I use both mean and median to describe a change?

Yes, it is common to use both mean and median to describe a change. They can complement each other and provide a more complete understanding of the data.

## 5. How do I know which measure to use when describing a change?

The measure of change to use depends on the nature of the data and the research question being addressed. It is important to consider the distribution and presence of outliers before deciding on the appropriate measure to use.