Properties of Mean, Standard Deviation

Question

Hi Guys,

Have my gmat in less than 36 hours and would appreciate help on the following:

Standard Deviation and Mean for a set of numbers

How does each change if: 
a. a certain number is added to all the numbers
b. a certain number is subtracted from all the numbers 
c. a certain number is multiplied with all the numbers 
d. all the numbers are divided by a certain number

Bunuel · Answer

If we add or subtract a constant to each term in a set: Mean will increase or decrease by the same constant. SD will not change. If we increase or decrease each term in a set by the same percent (multiply all terms by the constant): Mean will increase or decrease by the same percent. SD will increase or decrease by the same percent. Questions on this concept to practice: lately-many-questions-were-asked-about-the-standard-85896.html ps-questions-about-standard-deviation-85897.html if-q-is-a-set-of-consecutive-integers-what-is-the-standard-151794.html in-the-last-two-years-each-of-jeremy-s-six-children-grew-in-130614.html during-an-experiment-some-water-was-removed-from-each-of-94166.html set-a-consists-of-all-even-integers-between-2-and-110876.html if-d-is-the-standard-deviation-x-y-and-z-what-is-the-stan-93979.html what-is-sd-of-given-set-of-numbers-whose-average-is-104000.html there-is-a-set-of-consecutive-even-integers-what-is-the-98877.html Theory on Statistics and Sets problems: math-standard-deviation-87905.html All DS Statistics and Sets problems to practice: search.php?search_id=tag&tag_id=34 All PS Statistics and Sets problems to practice: search.php?search_id=tag&tag_id=55 Hope this helps.

brobeedle · Answer

Thanks Bunuel, so am I right to say that if all the terms are divided by the same constant, the effect is not linear - i.e., cannot be determined unless we calculate the st.dev of the new set as well?

Bunuel · Answer

No.

Multiplying is the same as dividing: for example, dividing by 2 is the same as multiplying by 1/2.

If we increase or decrease each term in a set by the same percent (multiply all terms by the constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.

Thus the above holds true for dividing as well.

Hope it's clear.

brobeedle · Answer

Thank you! Clear now

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bumpbot · Answer

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Properties of Mean, Standard Deviation

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