Question

Why is the mean considered the center of gravity of the distribution? Can you illustrate this principle with a simple income distribution?

Answer 1

Mean is one of the measures among the various measures of central tendency. As we know the calculation of mean is carried out by considering the values of all the data points, or we can say it incorporates all the points(values), it gives an overall output which summarises all the data into a point measure.
Mean perfectly balances all the values and gives us an average of all the values. the center of gravity refers to the point or measurement which balances all the weight and hence we can call mean as the center of gravity. This can also be verified by taking the deviation of values from the mean and summing them up computes to value equal to zero. Hence it signifies that the distance of all the points from mean is perfectly balanced.

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