We have a dataset: 13, 6, 13, 8, 2, 19, 11, 16, 17, with size n = 9.
We will add 32 to it.
In this case, the mean will be affected, as it depends on each individual value of the dataset. As the number is greater than all the numbers in the dataset, it will be greater than the actual mean. Then, the mean will increase.
The median may or may not change, depending on the values of the set.
Then, we can find the median before and after the addition.
First, we have to sort the data: 2, 6, 8, 11, 13, 13, 16, 17, 19.
The median, for a size n =9, will be located in the fifth place, so the median is 13.
Then, the dataset has 4 values below and 4 values above the median.
When we add 32, it will be the greatest value, so we will have a dataset of size n =10 and sorted as: 2, 6, 8, 11, 13, 13, 16, 17, 19, 32.
The median will be the average between the fifth and sixth place. Both values are 13, so the average, and therefore, the median will be also 13.
Then, in this case, the mean increases but the median does not.
Answer: The mean will increase and the median will remain the same.