There are a few properties of the mean. Let us look at two of them.
Property 1:
When a particular number is added to each term, the mean also increases by the same value.
Example 1: Consider the numbers 1, 2, 3.
- Finding the mean
1+2+3/3 = 6/3 = 2 ……..(i)
- Increasing the value of each term (1,2,3) by 2
1+2 = 3
2+2 = 4
3+2 = 5
- Finding the mean
3+4+5/3 = 12/3 = 4 ……. (ii)
- Comparing (i) and (ii) we find that when each term was increased by 2, the mean also increased by 2.
Example 2: Consider the numbers 1, 3, 8.
- Finding the mean
1+3+8/3 = 12/3 = 4 …….(i)
- Multiplying each term (1,3,8) with 4
1*4 = 4
3*4 = 12
8*4 = 32
- Finding the mean
4+12+32/3 = 48/3 + 16 ……. (ii)
- Comparing (i) and (ii) we find that when each term was multiplied by 4, the mean was also multiplied by As 4 multiplied by 4 is 16.
And the same goes for subtraction or division.
Property 2:
The sum of deviations of each term from the mean will always be zero.
Example: Consider the numbers 4,5,6 and 9.
- Finding the mean
- Finding the deviation
- Adding all the deviations