Definition
Arithmetic mode denoted by 'Mo', is the most frequently occuring value in a finite number of values. Average is calculated by counting all values in data and finding out value with highest count.

Formula MS Excel
In MS Excel, mode is calculated using "=Mode(Range)" function. Newer MS Excel versions have two additional formulas as well (Mode.SNGL and Mode.MULT). For example in the below demonstration a dataset of 1,1,1,2,2,2,2,3,3,4,5,5 has been defined in range A2:A13. In cell A14, we entered function "=Mode(A2:A13)" and the result is 2 which is the arithmatic mode of all those values.
For better understanding you can draw a chart. Create two more columns next to data namely Values and Frequency. In values column enter data by listing down values from 1 to 5. In next column enter frequency of each number. Now select frequency column including its heading and click on column chart in Insert>Charts tab. Now you can see frequencies of all numbers drawn on a chart and as you can see '2' has the highest frequency.

Python
In python you can use "statistics" liberary to perform arithmetic mode.
If you do not have python already installed, please download one with spider. Simplest ones are portable ones which do not need to be installed like winpython. You can download portable python from https://portablepython.com/
1. To import statistics type "import statistics as st"
2. You will also need pyplot liberary to draw a chart. Import pyplot using "import matplotlib.pyplot as pp"
3. Now define your data set as variable x using "x = [1,1,1,2,2,2,2,3,3,4,5,5]"
4. Now calculate Mean and store its value in variable "m", using "m = st.mode(x)"
5. You can display the value of mean computed above using print command. Type "print("Mode: " + str(m))"
6. For better understanding draw a bar chart of frequencies using "pp.bar(["1","2","3","4","5"],[3,4,2,1,2])"
7. In Spider, press Run and see the results. 