Question: Truth About Sets A & B

Comment on Truth About Sets A & B

I'm having trouble understanding something here...

I'm stuck on the evaluation of condition I. The example you used that makes this untrue, (I have the video paused at 1:18) has the numbers for set B as {1,2,6}. While this does make the combined set have a median of 5, those numbers don't meet the criteria for set B of having an average of 3. (1,2,6) has an average of 4.5, so we can't use those numbers as an example.

Any clarification would be appreciated.
greenlight-admin's picture

Average of {1, 2, 6} = (1+2+6)/3 = 9/3 = 3 (not 4.5)

Hello. Why couldn't the numbers in Set A be 1 and 9? Why can we make the assumption that the numbers in Set A have to be evenly spaced?
greenlight-admin's picture

Set A can, indeed, be {1, 9}, since the median would be 5.
I'm not sure why you feel that couldn't be the case.

Set A can have 5-5, 4-6, 3-7, 2-8, 1-9, whichever the case those are evenly spaced and mean will always be median, those are 5.

Hello, I had same question as above, however still confused with the "evenly spaced" part. Since theres only two positive integer how can you determine that it is evenly spaced?
greenlight-admin's picture

In order for the values in a set to be equally spaced (aka evenly spaced), the difference between any pair of consecutive values must always be the same.

For example, in the set {6, 10, 14, 18, 22} the difference between any pair of consecutive values is always 4. So, the values in the set are equally spaced.

Likewise, in the set {3, 8, 13} the difference between any pair of consecutive values is always 5. So, the values in the set are equally spaced.

Likewise, in the set {2, 5} the difference between any pair of consecutive values is always 3. So, the values in the set are equally spaced. Yes, there are only 2 values in this last set, but the principle remains the same.

As such, we can say that ANY set of two values can be considered equally spaced.
As such, the median of any 2 values will equal the mean of those 2 values.

Does that help?

Cheers,
Brent

I understood perfectly

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