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 as follows: 97, 97, 90, 53, 70, 97, 90, 70, 97, 97, 53, 90, 90, 97, 53.

a. Find the mean, median, mode, and midrange.

b. Which measure of central tendency was given in the advertisement?

c. Which measure of central tendency is the best indicator of the "average" in this situation?

The mean of the customer satisfaction percentages is 79.3%, the median is 90%, and the mode is 97%. The midrange is 75%. The median would be the best measure of central tendency in this case, as it is less affected by outliers.

Explanation:

Calculating Measures of Central Tendency

First, let's organize the sample percentages: 53, 53, 53, 70, 70, 90, 90, 90, 90, 97, 97, 97, 97, 97, 97.

To calculate the mean, add all the percentages together and divide by the number of samples:

Mean = (53+53+53+70+70+90+90+90+90+97+97+97+97+97+97) / 15 = 1189 / 15 = 79.3%

The median is the middle number in an ordered list:

Median = 90% (it's the eighth number in the list)

The mode is the most frequently occurring number.

Mode = 97%

To find the midrange, take the average of the highest and lowest percentages:

Midrange = (53 + 97) / 2 = 75%

The measure of central tendency given in the advertisement is the mean, as it refers to 'on the average.'

Considering the best indicator of the "average" in this scenario, the mean might be skewed due to the outliers, so the median would likely provide a better indicator, as it is less sensitive to extremes.