science!!! Diffcult!

I think "Mean" in your question refers to arithmetic mean. There are other "mean"s (such as geometry mean and harmonic mean) in statistic but this is the most widely used.

All 3 are used in statistic to measure the central tendency of data. They all focus on where the data is centered or clustered.

Assuming all data are integers:
Mean is the average calculated by adding all numbers and divided by the number of integers.
Medium is the number which half of the integers are smaller than the medium and half of the integers are larger than the medium.
Mod is the integer that appears most in this set of data.

For example, consider the following data set:
10, 10, 20, 30, 10000

total number of data is 5
mean is (10 + 10 + 20 + 30 + 10000) / 5 = 2014
medium is 20
mode is 10

Normally, arithmetic mean is good enough. It is used in areas such as MTBF (mean time between failures). MTBF is used in almost all electronics and it is an important data for manufacturer to issue warranties.

The other measure "medium" can be used in conjunction with mean to give a better picture of the data. From the example above, the mean is 2014 but the medium is just 20. It is obvious from these numbers there exists a very large integer in the data set.

The measure "mode" represents the concentration of data and can be used in service industries to help them targeting potential customers.

Besides wiki, I have found the following website with a very interesting example of how these 3 are used.

MEAN: the average no.
Median:the middle of numbers
Mode: the no. which appear the most