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12 Jan 2023, 01:59
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What is the difference between the mode and the median of a list of integers?
1. The difference between any two integers in the list is less than 3.
2. The arithmetic mean of the list is equal to the mode of the list.
1. The difference between any two integers in the list is less than 3.
2. The arithmetic mean of the list is equal to the mode of the list.
14 Jan 2023, 23:37
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Aabhash777
Mode: the number used maximum times in a set. Will always be a part of the set.
Median: the central value. May or may not be a part of the set.
1. The difference between any two integers in the list is less than 3.
So the numbers would be x-1, x and x+1. However, it is possible that only two of these three or just one of these three are in the list.
The difference between mode and median can be 0. x,x,x,x
It could also be 1/2. x-1, x-1, x, x+1
Insufficient
2. The arithmetic mean of the list is equal to the mode of the list.
Various possibilities.
1,1,2,2,2,3,3……|median-mode|=0
-10,-1,-1,1,2,3….median=0, mean=mode=-1, |median-mode|=1
Combined
Following observations
a) Mean is in the list as mode=mean.
b) the numbers are x-1, x, x+1
c) Only possibilities
#all same, say x,x… Median=mode=mean. Hence, |median-mode|=0
#two different….Not possible as mean will not be in the set.
#all three…..x-1,x-1……,x,x….x+1,x+1…
The mean has to be x, so mode is also x. Now, the numbers of x-1 and of x+1 will have to be equal to give mean as x.
Thus, x-1 and x+1 in equal numbers means x is more in number and in middle. Thus median will also be x, even if total elements are even or odd.
|median-mode|=0
Sufficient
C
10 Jan 2026, 15:45
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