Question

A={-2,3,6,8,13,20}

For distribution A for each observation calculate the deviations then add the deviations together. Explain briefly why the mean is the balance point.

Answer 1

Mean= (-2+3+6+8+13+20)/6=48/6=8

So, the required deviation= {(-2-8),(3-8),(6-8),(8-8),(13-8),(20-8)}= (-10,-5,-2,0,5,12)

So, sum of deviations= (-10-5-2+5+12)= 17-17= 0

Here, the mean is balance point as the deviation just after mean and below means same with unequal sign and they cancelled each other deviation and makes some 0. And also one reason behind this is that the square of deviation taken about mean is minimum so, we consider it as a balance point.