Mean / Median / Mode

Mode
is like the most often occurring value in your set of data
i.e. Dataset: 1, 2, 3, 3, 4 -> Mode is 3

There can also be multimodal datasets. Eg. 1,2,2,3,3. Here the mode is 2 and 3.

Median
is the value in the middle of your data set. (values have to be ranked from low to high)
i.e. Dataset: 1, 2, 3, 3, 4 -> Median is 3
if there is no middle number for example in a dataset of 1,2,3,3 then you take the average of the 2 middle numbers (eg. 2 and 3)
Therefore (2+3)/2= 2,5 is the Median

Mean
is the average value of your dataset. You calculate the sum of the values and divide them by the number of values
i.e. Dataset 1,2,3,3,4 -> Mean is 13/5= 2,6
(1+2+3+3+4 = 13 and 1,2,3,3,4 = 5 values)

Frequently the average (mean) is draged to one side by an outlyer. Eg. 1,2,3,3,100 = 109/5 = 21,8 is the mean. Therefore even if 4 out of 5 values (1,2,3,3,100,) are within the range of 1-3 the average value of 21,8

Conclusion

As you can see, while the mean and median (eg. 2,5 and 2,6) dont necesarrily have to occur in the dataset. The mode is always representet within the dataset. One further advantage of the mode is that you can use the mode also with nearly all kinds of data.

Mean can only be used with ratio and interval data.
Median can be used with ordinal, ratio and interval data. As nominal data cant be put in a meaningfull order (eg. names) one cant calculate the mean or median.