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Which of Three Statistics Would Change?

Discussion in 'CAT/MAT/GMAT Preparation' started by Royaluni, Sep 11, 2015.

  1. Royaluni

    Royaluni Administrator

    GMAT Practice Question- A researcher computed the mean, the median, and the standard deviation for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change.

    A. The mean only

    B. The median only

    C. The standard deviation only

    D. The mean and the median

    E. The mean and the standard deviation

    Answer- theoretically if 5 is added to each number, mean and median will go up by 5 whereas standard deviation will remain same because that depends upon the spread of the numbers and it will remain same if all numbers are moving equally.

    We can also select smart numbers to apply this theory;

    Now we are dealing with 5 so let’s assume a good number which can be used easily with 5.

    Let’s assume there are total 5 numbers and each with value 5. Total would be 25 and mean will be 5;

    Mean = total /numbers of items = 25/5 =5

    Median = value of middle number i.e. 5

    Standard deviation = squares of variance

    Variance = square of the difference of each number from mean / total number of items

    In order to find the variance of all the numbers, we will add all the numbers after calculating the square of the difference for each number.

    Mean is 5 and all the numbers in the set are 5, therefore difference is 0. Square of 0 is 0 and when you divide 0 by 5, you get 0.

    Standard deviation = Square of 0

    = 0

    Now if we add 5 to each number, each number become 10 and now;

    Mean = 10+10+10+10+10/5=50/5=10

    Median = 10

    Standard Deviation = 0

    As you can see, the variance i.e. difference of the each number from mean remains same therefore standard deviation remain same but mean and median has changed, so our answer is;

    D. The mean and the median

    how many times the average (arithmetic mean) of its revenues in November and January

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