LEAP Administrator 5 years ago Problem Solving | Statistics
If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers? (more)
If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?
(A) (Q - 1)/2 120
(B) Q/2 119
(C) Q/2 120
(D) (Q 119)/2
(E) (Q 120)/2
Let the first term be x
The largest term will be x + Q - 1
Median = (Q+1)/2 th term
Since the numbers are consecutive Median = x - 1 + (Q + 1)/2
120 = x - 1 + (Q+1)/2
x = 121 - (Q+1)/2
Largest term = x + Q - 1 = 121 - (Q+1)/2 - 1 = 120 + Q - Q/2 - 1/2 = 120 + (Q-1)/2
A is correct
LEAP Administrator 5 years ago Problem Solving | Statistics
A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ? (more)
A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m d ?
Ref. to the figure:
the question says the shaded portion between m-d and m+d = 68%
that means unshaded portion = 100 - 68 = 32%
since the curve is symmetric
% of population greater than m+d = 32/2 = 16%
the percentage of population below m+d = 100 - 16 = 84%
