Imade a distribution of 15 apartment rents in my neighborhood. one apartment had a higher rent than all the others, and this outlier caused the mean rent to be higher than the median rent. does this make sense because the outlier with a large value increases the mean, but does not affect the median?

Yes this makes sense

Step-by-step explanation:

When their is one outlier it makes the average spike which can present misleading data while with median the outlier is left relatively unaffected.

Yes this makes sense.

Step-by-step explanation:

The given dataset consists of 15 apartment rents. A data value which is an outlier (much larger than the rest) will increase the overall mean value of the population but it may not affect the median. Let us take an example of 15 sample rent value in ascending order,

100,120,130,140,150,170,175,185,190,200,220,250,280,290,1000

Here , mean rent will become high due to the single high rent datapoint(1000) but the median won't be impacted.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1