Standard deviation

Question 1

If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.

If we increase or decrease each term in a set by the same percent (multiply by a constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.

Question 2

For a set X containing n integers, is the mean even?

(1) n is even.
(2) All of the integers in set X are even.

I was confused between C and E

Answer 2

For a set X containing n integers, is the mean even?

The mean of a set = The sum of the elements / number of elements, so the question is whether mean=sum/n=even.

(1) n is even –> mean=sum/even. Not sufficient.
(2) All of the integers in set X are even –> so the sum of the elements is even –> mean=even/n. Not sufficient.
(1) +(2) The question becomes whether mean=even/even=even, which can not be determined as even/even could be even (for example 4/2=2=even), could be odd (for example 6/2=3=odd) or could be non-integer (for example 6/4=3/2). Not sufficient.

Answer: E.

Question 3

The sum of the positive integers from 1 to 27 is equivalent to the sum of the integers from

A. -27 to 54
B. 0 to 28
C. 15 to 45
D. 38 to 46
E. 48 to 54

Answer 3

Sum of Numbers = Average * Number of numbers
If numbers are from 1 to 27, average will be the middle number 14.
Sum of numbers = 14 * 27

We need to find the option where the sum is the same.

A. -27 to 54
-27 to -1 will cancel out numbers from 1 to 27. So the sum would be the sum of numbers from 28 to 54. These will be 27 numbers but with a much higher average. So ignore this option.

B. 0 to 28
Here the sum will be 28 more than our desired sum. Ignore this option.

C. 15 to 45
Here we have 31 numbers with an average much more than 14. So the sum will be much more than the desired sum. Ignore.

D. 38 to 46
Here we have 9 numbers with an average of 42 (the middle number).
Sum = 42 * 9 = 14 * 27 (matches)
This is the answer.

E. 48 to 54
Just to complete the calculations, let me show you how you can compare this option too.
Here we have 7 numbers with an average of 51.
Sum = 7 * 51 = 14 * 51/2 = 14 * 25.5. This is less than the desired sum.

Answer (D)

Question 4

Both sets are evenly spaced, thus their median=mean:

Question 5

X, 81, 73, 71, 98, 73, 64

What is the value of X in the above list of 7 numbers?

(1)  The average (arithmetic mean) of these 7 numbers is 80.
(2)  The range of these 7 numbers is 36.

Answer 5

Ans = A

from statement (2), the range of 36 can be either (98-x) or (x-64), and the value of x can be either 32 or 100 respectively –> insufficient

Question 6

Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?
	m
	10m/7
	10m/7 – 9/7
	5m/7 + 3/7
	5m

Answer 6

Ans = C

I missed the point that all numbers are distinct

Question 7

Alan’s regular hourly wage is 1.5 times Barney’s regular hourly wage, but Barney gets paid at twice his regular wage for any hours he works on Saturday. Both men work an integer number of hours on any given day. If Alan and Barney each worked for the same total non-zero number of hours last week, and earned the same total in wages, which of the following must be true?

I. Alan worked fewer hours Monday through Friday than did Barney.
II. Barney worked at least one hour on Saturday.
III. Barney made more money on Saturday than did Alan.

A.I only
B. II only
C. I and II only
D. I and III only
E. II and III only

Answer 7

Ans = b