Answers:
- Part (a): It stays the same
- Part (b): It decreases by 5 dollars
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Step-by-step explanation:
Part (a)
The numbers are sorted from smallest to largest, so we pick out the middle most value to get the median. It turns out that 1015 and 1025 are tied for the middle-most spot. Average these values to get (1015+1025)/2 = 1020. The median is 1020.
Notice how the median will not change if we replaced one "1100"s with "1060". This is because 1015 and 1025 still occupy the middle, and 1020 is at the midpoint between them. The median would only change if we either introduce or take away a value entirely, or if we replaced 1100 with some value between 1015 and 1025 that isn't 1020 itself. For instance, if we replace 1100 with 1019, then the median would become 1017 (decrease).
However, none of these situations happen, so that's why the median stays where it is.
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Part (b)
Go back to the original list of numbers.
Add them up to get
820+910+945+1015+1025+1085+1100+1100 = 8000
Divide this over 8 since we have 8 values here
8000/8 = 1000
The mean rent is $1000
Now let's replace one copy of the "1100" with "1060". Follow the same steps as above.
- Add: 820+910+945+1015+1025+1085+1060+1100 = 7960
- Divide: 7960/8 = 995
After that rent change from $1100 to $1060, the mean rent is now $995
The mean rent went down by 1000-995 = 5 dollars.