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The median of a set of 9 consecutive integers is 15. What is the largest integer?
17
18
19
20
19
For any odd number of consecutive integers, the largest integer is simply the median plus half of (n-1). Here, 15+(9тИТ1)/2=15+4=19.
Total number of consecutive integers (n) = 9. The median of the set is 15.
L=M+2nтИТ1тАЛ
For any odd number of consecutive integers, the largest integer is simply the median plus half of (n-1). Here, 15+(9тИТ1)/2=15+4=19.
Students often try to form an algebraic equation x+(x+1)+...=15 or incorrectly assume the median is the 5th number from the start but miscalculate the offset from the median to the last term.
Identify the position of the median
In a set of n=9 consecutive integers, the median is the middle term, which is the (2n+1тАЛ)-th term.
29+1тАЛ=5th┬аterm
Relate median to the largest integer
Since the sequence is consecutive, the largest integer is the median plus the number of steps required to reach the last (9th) position from the middle (5th) position.
9тИТ5=4┬аsteps┬аaway
Calculate the largest integer
Adding the 4 steps to the median value of 15 gives the final result.
15+4=19
C is correct because for a set of 9 consecutive integers with a median of 15, the terms are 11, 12, 13, 14, 15, 16, 17, 18, 19, making 19 the largest.
This concept is a special case of Arithmetic Progression where the common difference d=1. Always remember that for any AP with an odd number of terms, Median = Mean.
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