Hello, I thought I understood problem number 2 from today’s quiz, but I am still confused, will you please explain how we know what the other possibility could be for x in order for median and mean to be the same?
This question, right?
If 2 was the median here, then the numbers would be 1, x, 2, 4, 5 or x, 1, 2, 4, 5 in ascending order, right?
If we know that mean/median are equal, instead of doing sum = \textrm{mean} \times \textrm{number of values}, we can instead do sum = \textrm{median} \times \textrm{number of values}.
So, we know that the sum needs to be 2 \times 5 = 10. We also know that the sum needs to be 1+2+x+4+5 or 12+x.
So, now we can set up 12+x = 10, and figure out that x must be -2.
Hope that makes sense. As a challenge, try and find another possible x value.
Hint: set the median to be 4 this time!
Yes, this is it. Thank you very much for your help. It makes a lot more sense now!
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