Answer:
To answer the question, let's calculate the median and mean of the given salaries.
The median is the middle value when the data is arranged in ascending order. In this case, the middle value is 737 since there are an odd number of values.
The mean is calculated by summing all the values and dividing by the number of values. Let's calculate it:
Sum of salaries = 547 + 596 + 647 + 655 + 737 + 745 + 750 + 780 + 834 = 6591
Number of salaries = 9
Mean = Sum of salaries / Number of salaries = 6591 / 9 = 732.33 (rounded to two decimal places)
Now, let's see what happens when the $834 salary changes to $1005.
(a) What happens to the median?
The median remains the same. Changing one value in the data set does not affect the position of the middle value.
(b) What happens to the mean?
To calculate the new mean, we need to subtract the old value ($834) and add the new value ($1005) to the sum of salaries:
New sum of salaries = 6591 - 834 + 1005 = 6756
New mean = New sum of salaries / Number of salaries = 6756 / 9 = 750.67 (rounded to two decimal places)
Therefore, the mean increases by $18.34.
So, the answer to (a) is "It stays the same" and the answer to (b) is "It increases by $18.34".
Explanation: