Mean/Median/Standard Deviation quick question

Question

Hi Guys This is a bit last minute - my exam is in less than 12 hours from now :shock:

Can you help me with the following 2 concept related questions pls? If each number in a group of numbers is increased by the same constant AMOUNT, how does the mean, median and standard deviation change? Also, if each number in a group of numbers is increased by the same constant PERCENTAGE, how does the mean, median and standard deviation change please? If the 29th of july 2015 is a Wednesday, what would the 29th (or any other day) of the year 2033 be? B

Bunuel · Answer

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 lately-many-questions-were-asked-about-the-standard-85896.html ps-questions-about-standard-deviation-85897.html Check other Standard Deviation Questions in our Special Questions Directory .

ENGRTOMBA2018 · Answer

Bunuel has already posted links to various sets related theory.

For the sake of completeness, below are the answers for your questions:

1. If each number in a group of numbers is increased by the same constant AMOUNT, how does the mean, median and standard deviation change?

Mean will become = Old mean + Amount  ,

You can look at it like this:

Lets say your original mean = M = Sum of all the elements / n ---> M =S/n . Now when you add a fixed amount (say 'a') to all the elements, the new sum becomes: S+n*a and the new average becomes: Mn (new average) = (S+na)/n = S/n + a = M +a .

Thus the mean changes to old mean + AMOUNT.

ii) Median will be increased by 'a'

Median is the center most term and as you are adding a CONSTANT AMOUNT , all the elements will be 'shifted' by 'a' and hence the middle most term will become OLD MEDIAN + a

Thus  NEW MEDIAN = OLD MEDIAN + a

iii) Standard deviation

Here are the rules for SD:

SD_new = SD_old  (when you add or subtract a value 'a')

SD_new = SD_old / a or SD_old *a  (when you divide or multiply by a value 'a')

2. Also, if each number in a group of numbers is increased by the same constant PERCENTAGE, how does the mean, median and standard deviation change please?

A percentage can be treated as an additional number 'a' multiplied to the original elements. LEts say you have a set : {1,2,3} and then you increase all by 10% ---> In effect, you are multiplying ALL the elements by 1.1.

Thus based on rules mentioned in (1)

Mean_new = Mean_old * a  .

Look at it this way:

Lets say your Mean_old = Sum / n ---> Sum_new with all elements multiplied by a (can be integer or fraction) = Sum_old * a ---> Mean_new = Sum_new / n = Sum_old * a /n = Mean_old*a

Median_new = Median_old * a  (as Median is only the middle most value of an ordered set!).

Finally,  SD_new = SD_old / a or SD_old *a

Hope this helps.

All the best for your GMAT.

KarishmaB · Answer

Though, you are done with your exam, here is a useful concept for other people who come across this thread.

When you talk about mean/median/SD of a list of numbers, imagine the numbers lying on the number line. 
When you add the same positive number to all the elements, the entire bunch moves ahead together on the number line.

The mean lies somewhere in the middle of the bunch and will move by the added number.

The median is the middle number and will move ahead by the added number.

The SD is a measure of dispersion of the numbers around the mean and the dispersion will not change when the whole bunch moves ahead as it is. So SD will stay the same.

EMPOWERgmatRichC · Answer

Hi brobeedle,

How did you score on your GMAT? Did the information in this thread end up factoring into your performance on Test Day?

GMAT assassins aren't born, they're made,
Rich

bumpbot · Answer

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Mean/Median/Standard Deviation quick question

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Mean/Median/Standard Deviation quick question

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