Question

A set of 15 different integers has a median of 25 and a range of 25. What is the greatest possible integer that could be in this set?

Answer 1

A set of 15 different integers has a median of 25 and a range of 25. What is the greatest possible integer that could be in this set?

Answer: We are given the median of 15 different integers = 25, which means there are 7 observations below 25.

To make the greatest number as greater as possible, these 7 numbers should cost the range as little as possible.

They will be 24,23,22,21,20,19,18

Therefore, the greatest value that can fill the range is 18 + 25 = 43

Hence, the greatest possible integer that could be in this set is 43.

Answer 2

The greatest possible integer in the set could be 43.

Step-by-step explanation

Range is the difference between largest and smallest terms in the set. That means...

`Range= Largest - Smallest\\ \\ or, Largest= Range+Smallest`

Now for getting the maximized largest number, we need to maximize the smallest number as the range 25 is fixed.

As the set has total 15 terms, so the median will be the 8th term. That means, there will be 7 terms before the median 25.

So, the maximized smallest number will be: 25 - 7 = 18 (As all the terms are different integers)

Thus, the possible greatest number
`= Range+ 18= 25+18=43`