Bunuel wrote:

In a set of twenty numbers, 19 of the 20 numbers are between 40 and 50. Is the median greater than the mean?

(1) The standard deviation is greater than 15

(2) The 20th number is greater than 100

Kudos for a correct solution.

(1) The standard deviation is greater than 15

mean and median of the 19 elements are within 40-50.

Standard deviation of 19 elements will be minimum (0) when all 19 elements are same .

Standard deviation of 19 elements will be maximum when there are 10 50s and 9 40s . Roughly 5.

adding 1 new element to this set has caused the standard deviation to go up .

2 cases ,

a) the 20th element is less then all the 19 elements. it can be -1000 , -2000 etc. Mean will move on left side with median standing taller than mean on the histogram.

b) the 20th element is greater then all the 19 elements. it can be 1000 or any big number. Mean will move on right side with mean greater than the median .

(2) The 20th number is greater than 100

as 100 is a large number compared to remaining 19 elements so the mean will move towards right by a big magnitude, causing median to be less than the mean.

Sufficient.

Answer should be B.

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Lucky

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