Hi everyone,
I recently reviewed the following question but still haven't quite understood the answer explanation:
"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: Q2 + 120
D: Q+119/2
E: Q+120/2
Answer Explanation:
For an odd number of data values, the median is the middle number. Thus, 120 is the middle number, and so half of the Q-1 remaining values are at most 120 and the other half of the Q-1 remaining values are at least 120. In particular, Q-1/2 data values lie to the right of 120 when data values are listed in increasing order from left to right, and so the largest data value is 120+Q-1/2 (Answer A).
My question:
I fully understand, that Q-1/2 values of the remaining Q-1 values lie to the right of 120. However, Q could be 7 (Values)and thus, 3 values would lie to the right of 120. Since we do not know these values, these could be 290, 345, 900 or whatsoever... In this case then, 900 would be the largest of the 7 integers. BUT, the correct answer (A) would give me a value such as 7-1/2 +120 = 120 +6 = 126.
Can anyone out there help me out on this one?
I'd appreciate your help.
Kind regards,
Tobi
I recently reviewed the following question but still haven't quite understood the answer explanation:
"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: Q2 + 120
D: Q+119/2
E: Q+120/2
Answer Explanation:
For an odd number of data values, the median is the middle number. Thus, 120 is the middle number, and so half of the Q-1 remaining values are at most 120 and the other half of the Q-1 remaining values are at least 120. In particular, Q-1/2 data values lie to the right of 120 when data values are listed in increasing order from left to right, and so the largest data value is 120+Q-1/2 (Answer A).
My question:
I fully understand, that Q-1/2 values of the remaining Q-1 values lie to the right of 120. However, Q could be 7 (Values)and thus, 3 values would lie to the right of 120. Since we do not know these values, these could be 290, 345, 900 or whatsoever... In this case then, 900 would be the largest of the 7 integers. BUT, the correct answer (A) would give me a value such as 7-1/2 +120 = 120 +6 = 126.
Can anyone out there help me out on this one?
I'd appreciate your help.
Kind regards,
Tobi
.
