Statistics and Sets Problems

[swerve]

Set \(S\) consists of consecutive positive integers. If the lowest integer in Set \(S\) is \(1\) and the sum of the integers os Set \(S\) is 231, what is the median of Set \(S\)?

A. 10.5
B. 11
C. 12
D. 13
E. 22

The OA is B

Source: Magoosh

[Scott@TargetTestPrep]

Set \(S\) consists of consecutive positive integers. If the lowest integer in Set \(S\) is \(1\) and the sum of the integers os Set \(S\) is 231, what is the median of Set \(S\)?

A. 10.5
B. 11
C. 12
D. 13
E. 22

The OA is B

Source: Magoosh

If we let x = the largest integer in set S, we can create the following equation using the formula average * quantity = sum:

(1 + x)/2 * (x - 1 + 1) = 231

(1 + x)/2 * x = 231

x + x^2 = 462

x^2 + x - 462 = 0

(x + 22)(x - 21) = 0

x = -22 and x = 21

Since x is positive, x = 21. Since the median of set S is also the average of set S, the median of set S is (1 + 21)/2 = 22/2 = 11.

Answer: B