a set of five distinct positive integers has a mean of 1000 and a median of 100. what is the largest possible integer that could be included in the set?



Answer :

The largest possible integer or maximum value that could be included in the set is 4897.

The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list. This usually means average.

The median is the middle value of the list ordered from smallest to largest.

Mode is the most frequently occurring value in the list.

Numbers x1,x2,x3,x4 and x5 (these are in numerical order.)

We know that (x1+x2+x3+x4+x5) / 5 = 1000. This is equivalent to x1+x2+x3+x4+x5 = 5000.

Also, the median of (x1,x2,x3,x4,x5) is (x3) = 100. So x3=100.

x1+x2+100+x4+x5=5000

x1+x2+x4+x5=4900

Since x1, x2,x4 are positive,

The maximum value of x5 is 4897.

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