Mean and Median questions

[flyhighx]

Hi,
Can someone please explain in full detail and the right terminology for:
How does the mean differ significantly from the median, discuss

Thanks!

[brenden]

Well, the mean is the average score of a set of data. Let's say the data below is the time in seconds it takes a group of ten people to run 100 metres.
1. 14
2. 15
3. 16
4. 16
5. 15
6. 14
7. 28
8. 27
9. 31
10. 29

The mean (sum of data divided by number of data points) here is 20.5. Notice the higher values toward the end data points. So the mean will take into account all the data points and then just reflect the average value. It won't necessarily give you a measure of centre when the data is skewed, although, it will give you an accurate measure of centre if you have symmetrical data.

Take the same set of data, and we will look for the median (the middle number). The middle number is referring to whatever value lies in the middle of however many data points there are, assuming your data points are ordered. This can be found with (n+1)/2, where n is equivalent to the number of data points. For our above set of data, we have 10 data points. Thus, (10+1)/2 = 5.5 will be our number. So, whatever number is between the values at data point 5 and data point 6 (because 5.5) will be the media. Let's order the list.
1. 14
2. 14
3. 15
4. 15
5. 16
6. 16
7. 27
8. 28
9. 29
10. 31

We can see that the median will be 16, because data points 5 and 6 are at that value. If data point 6 had a value of 17, then the median would be 16.5. If it were 20, the median would be 18 - exactly in the middle of data point 5 and 6.

The median, then, will always give as an accurate measure of centre, and will not be influenced by extreme values (outliers), whereas the mean will be very influenced by outliers. Thus, we would always use the median as our measure of centre when we are facing extreme values, or if the data set was skewed one way or the other. You can see by the variance of my mean and median, 20.5 and 16 respectively, that my data is positively skewed (because the mean is significantly higher) - so it's more appropriate to use the median as a measure of centre.


Tl;dr

Mean = the average
Median = the middle number.

[Yacoubb]

The mean is the calculated average or balance point of a set of data. The median on the other hand is the central middle value where 50% of the data lies on one side of the median, and 50% of the data lies on the other half.

What you are required to understand in data analysis is that the median is usually a more reliable summary statistic than the mean. The median is unaffected by the presence of outliers & if the distribution is skewed; the mean is affected by both outliers and skewing of distributions of data.

Therefore, if you are analysing a histogram for instance that is approximately symmetric with no apparent outliers, you can state that using both the mean and median is appropriate as the mean value cannot be affected by any of the factors we mentioned above.

- In a positively skewed distribution, mean > mean
- In a negatively skewed distribution, mean < mean
- In a symmetric distribution, mean = mean.

By simply calculating both of these summary statistics & comparing them, you can see that if the difference between the mean & median is minimal, the distribution is approximately symmetric with no apparent outliers. However, if you see a marginal difference in the value of the mean & median, there is something (i.e. skewing AND/OR outliers) that is evidently impacting upon mean value.

Hope this helps