Question

Which one of the tools of dispersion seems to be the best one to use between the range, variance and standard deviation? What is the benefit of know how spaced the scores are in an analysis?

Answer 1

Answer:

OUT of the mentioned three tools of dispersion RANGE is the worst performer can will tell us the least about the spacing of the data as RANGE IS MAXIMUM VALUE - MINIMUM VALUE

SO EVEN IF WE CHANGE THE MIDDLE VALUE BY KEEPING EXTREME VALUES SAME RANGE DOES NOT CHANGES SO RANGE IS THE WORST.

NOW OUT OF VARIANCE AND STANDARD DEVIATION

STANDARD DEVIATION IS THE BETTER ONE IN THE CONTEXT OF THE PROBLEM ASKED

so STANDARD DEVIATION (S.D) IS THE BEST OUT OF ALL THREE

IT IS DUE TO THE FACT THAT S.D IS OF THE SAME ORDER AS OUR OBSERVATIONS ARE BUT VARIANCE IS OF SQUARE ORDER

MEANING IF WE MULTIPLY EACH OBSERVATION BY 2

THEN TECHNICALLY spacing between the observation only changes by a factor of 2 but variance changes by a factor of 2^2 that is 4.

THE BENEFIT OF KNOWING HOW SPACED THE SCORES ARE ..

helps us to know the distribution of the scores (or how they diverse they are) that will help us in many analytical problems like

ESTIMATION , PREDICTION, OUTLIER DETECTION AND many more.

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