The average of 100 numbers is 6, and the standard deviation is D, where D is positive. When added which of the following numbers, the new deviation will be less than D?

A. -6 and 0

B. 0 and 0

C. 0 and 6

D. 0 and 12

E. 6 and 6




standard deviation is a measure of how spread out the data are. in other words, the standard deviation gives you a rough idea of how far away the numbers are from the average (mean).

hence the name: standard (= typical) deviation (= difference from the norm). notice that standard deviation is not simply the average of how far away the data points are from the average, but that notion is more than sufficient for conceptual understanding.

in any case, you have no idea how big the standard deviation is. it could be something like 0.0000001, meaning that every number in the set is extremely close to the average value of 6. therefore, the only way to be absolutely sure you're reducing the standard deviation is to insert two numbers each of which is exactly the average. since these points are both 0 units away from the average, they will lower the standard deviation.

Answer - E