Final answer:
The median of the data set is 51, and the mode is 7.
Step-by-step explanation:
Median:
To find the median of a data set, you first need to sort the numbers in ascending order. The data set given is: 47, 51, 84, 33, 20, 17, 83, 23, 88, 96, 35. Arranging them in ascending order gives: 17, 20, 23, 33, 35, 47, 51, 83, 84, 88, 96. Now, to find the median, we look for the number that is exactly in the middle of the sorted set. Since there are 11 numbers in the set, the median will be the 6th number, which is 51. Therefore, the median of the data set is 51.
Mode:
The mode of a data set is the value(s) that appear(s) most frequently. In this data set, the number 7 appears the most times (3 times). Therefore, the mode of the data set is 7.