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------------------------------------------------ For the given data set, find the:

a. Mean
b. Median
c. Mode (or state that there is no mode)
d. Midrange

A company advertised that, on average, 97% of their customers reported "very high satisfaction" with their services. The actual percentages reported in 15 samples were the following: 97, 97, 90, 53, 70, 97, 90, 70, 97, 97, 53, 90, 90, 97, 53.

a. Find the mean

To find the mean of the given data set, we add all the values together and then divide by the number of values. The provided data set is: 97, 97, 90, 53, 70, 97, 90, 70, 97, 97, 53, 90, 90, 97, 53. Adding these together gives a sum of 1244. There are 15 values in total, so the mean is 1244 / 15, which equals approximately 82.93.

The median is the middle value when the data set is arranged in ascending order. For the same data set, after arranging it we have: 53, 53, 53, 70, 70, 90, 90, 90, 90, 97, 97, 97, 97, 97, 97. The median value, being the 8th number in this ordered list, is 90.

The mode is the most frequently occurring value in the data set. Looking at the ordered data, we find that 97 appears most often, precisely six times, making it the mode.

Lastly, the midrange is found by adding the smallest and largest values in the data set and dividing by two. So, midrange = (53 + 97) / 2 which equals 75.