tarek99 wrote:

A certain list of 100 data has a mean of 6 and a standard deviation of D, where D is positive. Which of the following pairs of data, when added to the list, must result in a list of 102 data with standard deviation less than D?

a) -6 and 0

b) 0 and 0

c) 0 and 6

d) 0 and 12

e) 6 and 6

Please explain your answer.

thanks

I think E 6,6 should be the answer.

sum of 100 numbers = 100 * 6 = 600

D = SQRT( 1/100 * summation of [(x[i] - 6) ^2 ]

with addition of 2 terms the total number of terms will be 102, so the bracketed part of SQRT above is already smaller,

My approach involves not increasing the summation part, and 6, 6 is ideal option for this

adding 6 + 6 to 600 = 612

mean will be 612/102 = 6..unchanged

since the added terms are 6,6 , the difference (6-6) = 0 and wont add to the summation part of SQRT above

thus SD will be smaller.