Question: Greatest of 5 numbers

Great question.
Since the mode is 4, we know that the first 3 numbers in the set are {4, 4, 5 ...}

At this point, the smallest integer we can add to the set is 6. If we were to add a number less than 5 then the median of the set will not be 5 (which is one of the requirements).

For example, if we add a 1, we get: { 1, 4, 4, 5, __} In this case, the median is 4.

Also, if we add another 5, we get: { 4, 4, 5, 5, __} In this case, the mode is 4 and 5.

So, in order for the median to be 5 and the mode to be 4, the next number we add must be greater than 5.

So, 6 is the smallest possible integer we can add to the set.

This is a medium-level question. I'd say it's in the 550-600 difficulty range.

Hi Dispy,

I just re-watched the video, and I feel that the explanation in the video is pretty much the same as the written explanation I provided for bakhtawer.
I'm not sure what else I would add to the original video.

Is there something in my written explanation that you feel isn't included in the video?

The median of {1, 4, 4, 5, 26} is 4. We need a median of 5.