Expert: Sherman D. - 7/30/2004

Question
Hi Dr. Sherman,

My question for you is about standard deviation.
This is a question from the GRE(Graduate Record Exam) Quantitative section:

1. Which is greater?:
(A) The standard deviation of the data 5, 5, 8, 14 and 18.

(B) The standard deviation of the data 6, 6, 8, 14 and 16.

The definition of Standard deviation is "the average distance from the arithmetic mean for the N measurments". So my study guide says. So if I apply this concept to the question above, first I must find the arithmetic mean of both data which is 10 for both(the sum of 5,5,8,14,18 devided by 6 is 10 for A; the same for B..). After this, what do I need to find out the standard deviation of (A) and (B)?

Thanks for your help!

Aes  

Answer
A.)
mean =
(5 + 5 + 8 + 14 + 18)/5 = 50/5 = 10

Variance =
((5-10)² + (5-10)² + (8-10)² + (14-10)² + (18-10)²)/5 =
((-5)² + (-5)² + (-2)² + (4)² + (8)²)/5 =
(25 + 25 + 4 + 16 + 64)/5 = 134/5 = 26.8

SD = sqrt(variance)
SD = 5.17687164

-----------------------------------------------------------

B.)
Mean = (6 + 6 + 8 + 14 + 16)/5 = 50/5 = 10

Variance =
((6-10)² + (6-10)² + (8-10)² + (14-10)² + (16-10)²)/5 =
((-4)² + (-4)² + (-2)² + (4)² + (6)²)/5 =
(16 + 16 + 4 + 16 + 36)/5 = (88/5) = 17.6

SD = sqrt(variance)

SD = 4.19523539

"A" is greater.

Info found at www.animatedsoftware.com/statglos/sgstdev.htm

Just to make sure, make sure to check to see if i didn't do anything wrong with my calculations.