Question

The monthly rents (in dollars) paid by 9 people are given below.
(Note that these are already ordered from least to greatest.)
765, 865, 880, 905, 1000, 1055, 1080, 1100, 1125Suppose that one of the people moves. His rent changes from $1125 to $945.
Answer the following.
What happens to the median?

Answer 1

To find the median of the rents before and after one person changes their rent from $1125 to $945, we need to consider the order of the rents.

Initially, the rents are:
765, 865, 880, 905, 1000, 1055, 1080, 1100, 1125

Since there are 9 values (an odd number), the median is the middle value, which is the 5th value in the ordered list:
- Median before the change: 1000

Now, after the person moves, the new set of rents becomes:
765, 865, 880, 905, 945, 1000, 1055, 1080, 1100

We then find the new median. Again, there are still 9 values, so the median is still the 5th value:
- The new ordered list is: 765, 865, 880, 905, 945, 1000, 1055, 1080, 1100

Now, the 5th value in this new ordered list is:
- Median after the change: 945

So the change in the median is:
- Median before: 1000
- Median after: 945

The median decreases from 1000 to 945 after the rent change from $1125 to $945.