35, 55, 40, 20, 24, 17, 22, 30, 12, 17, 4735, 55, 40, 20, 24, 17, 22, 30, 12, 17, 47a)Find the minimum value of the data set:b)Find the maximum value of the data set:c)Find the arithmetic mean of the data set:d)Find the median of the data set:Let's include one more data point in the data set. Suppose this new data value lies between the values 12 and 55, inclusively.e)Find the smallest possible value of the mean of the new data set:f)Find the largest possible value of the mean of the new data set:g)Find the smallest possible value of the median of the new data set:h)Find the largest possible value of the median of the new data set:

a) The minimum value of the data set is 12.

b) The maximum value of the data set is 55.

c) To find the arithmetic mean of the data set, you add up all the numbers and then divide by the number of numbers. The sum of the numbers is 473 and the total number of numbers is 20. So, the mean is 473/20 = 23.65.

d) To find the median of the data set, you arrange the numbers in order from least to greatest and then find the middle number. If there is an even number of numbers, you find the mean of the two middle numbers. In this case, there are 20 numbers, so the median is the mean of the 10th and 11th numbers, which are both 22. So, the median is 22.

e) The smallest possible value of the mean of the new data set would be if the new data point was 12 (the smallest number in the range given). In this case, the sum of the numbers would be 473 + 12 = 485 and the total number of numbers would be 21. So, the mean would be 485/21 = 23.1.

f) The largest possible value of the mean of the new data set would be if the new data point was 55 (the largest number in the range given). In this case, the sum of the numbers would be 473 + 55 = 528 and the total number of numbers would be 21. So, the mean would be 528/21 = 25.14.

g) The smallest possible value of the median of the new data set would be if the new data point was less than or equal to 22 (the current median). In this case, the median would still be 22.

h) The largest possible value of the median of the new data set would be if the new data point was greater than 22 but less than or equal to 30 (the next number in the ordered list). In this case, the median would be the mean of 22 and 30, which is 26.

a) The minimum value of the data set is 12.

b) The maximum value of the data set is 55.

c) To find the arithmetic mean of the data set, we add up all the numbers and then divide by the number of numbers. The sum of the numbers is 473 and there are 20 numbers, so the mean is 473/20 = 23.65.

d) To find the median of the data set, we list the numbers in numerical order and find the middle number. If there is an even number of numbers, we take the average of the two middle numbers. In this case, the numbers in order are: 12, 12, 17, 17, 17, 17, 20, 20, 22, 22, 24, 24, 30, 30, 35, 40, 40, 47, 47, 55, 55. The two middle numbers are 22 and 24, so the median is (22+24)/2 = 23.

e) The smallest possible value of the mean of the new data set would be if the new data point was 12 (the smallest number between 12 and 55). In this case, the sum of the numbers would be 473+12 = 485 and there would be 21 numbers, so the mean would be 485/21 = 23.1.

f) The largest possible value of the mean of the new data set would be if the new data point was 55 (the largest number between 12 and 55). In this case, the sum of the numbers would be 473+55 = 528 and there would be 21 numbers, so the mean would be 528/21 = 25.14.

g) The smallest possible value of the median of the new data set would be if the new data point was 12 or less. In this case, the numbers in order would be: 12, 12, 12, 17, 17, 17, 17, 20, 20, 22, 22, 24, 24, 30, 30, 35, 40, 40, 47, 47, 55, 55. The two middle numbers are 22 and 22, so the median is 22.

h) The largest possible value of the median of the new data set would be if the new data point was 55 or more. In this case, the numbers in order would be: 12, 12, 17, 17, 17, 17, 20, 20, 22, 22, 24, 24, 30, 30, 35, 40, 40, 47, 47, 55, 55, 55. The two middle numbers are 24 and 24, so the median is 24.