standard deviation problem

[maria08]

If m<2 and P = {1,2,3, m, 2m}
What could be the median of set P? Select all that apply.
A. 1
B. 2
C.3
D. m
E. 2m

Is there a smart way to approach this problem? Does it matter whether m is positive or negative?

thanks

[tommywallach]

m < 2 123 m 2m

Hey Maria,

This is a statistics question, specifically about the median. So you just need to think about what would affect the median. In other words, I want you (in the future) to try to answer your own question. Does it matter if m and 2m are negative?

Not technically. All that matters is if BOTH OF THEM are to the LEFT (on the number line) of 1, because that would then make the order this:

m 2m 1 2 3 -- in this case, the median is 1

This is possible, because they could be negative (OR, they could be something really small and positive, such as .1 and .2).

So what else could they be? Well, m could be smaller than 1 (for example .75), and then 2m would be larger than 1 (1.5, in this case):

m 1 2m 2 3 -- in this case, the median is 2m

Let's keep going. Now, the next thing we would want to try and create is this, because it would create a new median. Imagine that m is 1.6:

1 m 2 3 2m -- in this case the median is 2

Now let's see if we can make m the median:

1 2 m 2m 3 -- unfortunately, this isn't possible, because m would have to 2 or greater, and it can't be based on the constraints.

1 2 3 m 2m -- similarly, we can't do this, because now m would be 3 or greater, which it can't be.

So 1, 2, and 2m are our answers.

Hope that makes sense!

-t

[maria08]

I found this to be a rather tricky question but I like the way you broke it down and explained the various possibilities... thanks for that.

[tommywallach]

It's what I do!

-t