Arithmetic Mean:
The arithmetic mean, also known as the average, is a measure used to determine the central tendency of a set of numbers. It is calculated by summing up all the numbers in the set and then dividing the sum by the total number of elements in the set.

To find the arithmetic mean of the given set of numbers: 17, 32, 35, 33, 15, 21, 41, 32, 11, 18, 20, 22, 11, 15, 35, 23, 38, 12, we need to add up all the numbers and divide the sum by the total number of elements.

Sum of the numbers = 17 + 32 + 35 + 33 + 15 + 21 + 41 + 32 + 11 + 18 + 20 + 22 + 11 + 15 + 35 + 23 + 38 + 12 = 472

Total number of elements = 18

Arithmetic mean = Sum of numbers / Total number of elements = 472 / 18 = 26.22

Therefore, the arithmetic mean of the given set of numbers is 26.22.

Median:
The median is the middle value in a set of numbers when they are arranged in ascending or descending order. It is used to represent the central tendency of a dataset.

To find the median of the given set of numbers: 17, 32, 35, 33, 15, 21, 41, 32, 11, 18, 20, 22, 11, 15, 35, 23, 38, 12, we need to arrange the numbers in ascending order.

11, 11, 12, 15, 15, 17, 18, 20, 21, 22, 23, 32, 32, 33, 35, 35, 38, 41

Since the total number of elements is 18, the median will be the average of the two middle values. In this case, the two middle values are 22 and 23.

Median = (22 + 23) / 2 = 22.5

Therefore, the median of the given set of numbers is 22.5.

Mode:
The mode is the value that appears most frequently in a set of numbers. It represents the most commonly occurring value.

To find the mode of the given set of numbers: 17, 32, 35, 33, 15, 21, 41, 32, 11, 18, 20, 22, 11, 15, 35, 23, 38, 12, we need to identify the number that appears most frequently.

In this set, the number 32 appears twice, which is more than any other number. Therefore, the mode of the given set of numbers is 32.

Therefore, the arithmetic mean of the given set of numbers is 26.22, the median is 22.5, and the mode is 32.