Thanks Bunuel.
Bunuel wrote:
1. A set of data consists of the following 5 numbers: 0,2,4,6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?
(A) -1 and 9
(B) 4 and 4
(C) 3 and 5
(D) 2 and 6
(E) 0 and 8
The mean of the set is 4.
sqrt[((0-4)^2+(2-4)^2+(6-4)^2+(8-4)^2)/5] = sqrt[(16+4+4+16)/5] = sqrt(40/5) = sqrt(8)
The mean of set 0,8 is 4. Std.dev. is sqrt[(0-4)^2+(8-4)^2/2]=sqrt(8). Answer is E.
Bunuel wrote:
2. A certain list of 100 data has an average of 6 and 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 the standard deviation less than d?
(A) 0 and 6
(B) 0 and 12
(C) 0 and 0
(D) -6 and 0
(E) 6 and 6
E. If the set contained only 6 it's standard deviation would be 0. Since it is positive we can reduce the std.dev. by adding to integers equal to the mean - so answer is E.
Bunuel wrote:
3. For a certain examination, a score of 58 was 2 standard deviations below the mean, and a score of 98 was 3 standard deviations above the mean. What was the mean score for the examination?
(A) 74
(B) 76
(C) 78
(D) 80
(E) 82
2 eq in 2 unknowns. Let x denote mean and let y denote std.dev.
58 = x - 2y <=> x= 58 + 2y (1) AND
98 = x + 3y <=> 98 = 58+5y <=> y=8. Insert into (1) to get x=58+2*8= 74.
Answer is A.
Bunuel wrote:
4. Which of the following distribution of numbers has the greatest standard deviation?
(A) {-3, 1, 2}
(B) {-2, -1, 1, 2}
(C) {3, 5, 7}
(D) {-1, 2, 3, 4}
(E) {0, 2, 4}
A good way to go about these questions is to look for the range of the set compared to the number of elements in the set. Ceteris paribus it holds that the higher the range - the higher the std.dev and the higher the number of elements - the lower the std.dev. A is the only set with a range of 5 and only 3 numbers. Furthermore none of the numbers represent the average (0) and therefore all contribute to the std.dev. Answer is A.
Bunuel wrote:
5. Which of the following has the same standard deviation as {s,r,t}?
I. {r-2, s-2, t-2}
II. {0, s-t, s-r}
III. {|r|, |s|, |t|}
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
The absolute value of the numbers doesn't matter since it is the differences to the mean that enters into the std.dev. Thus I is the same as in the Q. The set in 2 is the set (s,s,s) subtracted by (s,r,t). This gives the same std.dev. as in set {s,r,t} (If you're in doubt try plugging in numbers. In III there is clearly a difference between the set {-1,1,1} and {1,1,1} so this does not necessarily have the same std.dev as {s,r,t}. The answer is D.
Bunuel wrote:
6. A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies one standard deviation d of the mean, what percent of the distribution is less than m+d?
(A) 16%
(B) 32%
(C) 48%
(D) 84%
(E) 92%
I am little uncertain about the meaning of this question. I will assume that you mean that 68% of the distribution lies one standard deviation above the mean (alternative interpretation is that 68% of the distribution lies within 1 std.dev from the mean).
The total mass of the distribution is 100%. Just subtract 68% from the total mass to get this rest = 32%. Answers is B.
Bunuel wrote:
7. Which of the following data sets has the third largest standard deviation?
(A) {1, 2, 3, 4, 5}
(B) {2, 3, 3, 3, 4}
(C) {2, 2, 2, 4, 5}
(D) {0, 2, 3, 4, 6}
(E) {-1, 1, 3, 5, 7}
Use the same principle I described above. All sets have 5 numbers. E have the larges range, and D comes in second. A has the third largest range and greater dispersion among numbers so answer is A.
OK, gotta hit the sack now. Thanks again for the questions Bunuel.