Answer: so as to spread out the differences
Step-by-step explanation: if we try to take the algebraic sum of each data set, negative and positive number of the same value cancels out.
If we try to take the modulus of the data set to have an absolute value, and sum up the answer, that gives us the mean deviation.
But by taking the square of the deviations (and taking the square root at the end) allows for more spread of the data set which gives a better results.
Let us test this with some number.
Assuming the data set
2, 3, 1.... The mean is 2
By taking algebraic sum of deviation, we have
(2-2) + (3-2) + (1-2) = 0 + 1 - 1 = 0
You can see 2 and -2 canceling out each other.
If we take the absolute value of deviation and sum it up, we have the mean deviation ( which is not important for this question, so we won't bother doing it)
For sum of squares of deviation, we have
(2-2)² + (3-2)² + (1-2)² = 1 + 1 = 2
√2 = 1.4142
As we can see from our value it is alot more detailed and spreads better
