Problem:
In the following list of numbers, the integer n appears n times in the list for 1≤n≤200.
1,2,2,3,3,3,4,4,4,4,...,200,200,...,200
What is the median of the numbers in this list?
Answer Choices:
A. 100.5
B. 134
C. 142
D. 150.5
E. 167 Solution:
There are
1+2+3+⋯+200=2200⋅201=20,100
numbers in the list, so the median is the average (mean) of the two middle numbers, the 10,050 th and 10,051st entries. The number of entries less than or equal to n is
1+2+3+⋯+n=2n(n+1).
Setting
2n(n+1)=10,050
and solving for n suggests that n is a little less than