We have a list of numbers: 352, 424, 443, 457, 493, 508, 570, 625.
a) The mean wil be the average of all the numbers, which can be calculated as the sum of all of them divided by 8, which is the quantity of data points.
Then, if we change 352 for 440, the sum of the all the numbers will increase, and therefore, so will the mean.
Then, if we change 352 by 440, the mean will increase.
The amount will be equal to the difference between 440 and 352, divided by 8:
[tex]\Delta\bar{x}=\frac{1}{8}(440-352)=\frac{1}{8}\cdot88=11[/tex]The mean will increase by 11 units.
b) In the case of the median, it will only change if we replace a number at one side of the median (left or right) with another number that will fall on the other side of the median.
In this case, if we replace 352 with 440, both will be in the same side in respect to the median (both will stay at the left of the median, which is 475, the average between 457 and 493).
Then, in this case, the median stays the same.
Answer:
a) It increases by 11.
b) it stays the same.