Final answer:
The mode of the Drama Club students is 17, the median is 16, and the calculated mean is approximately 16.3 years. Therefore, the first two statements are true and the third is false.
Step-by-step explanation:
The question involves understanding and applying concepts of statistics, specifically the mode, median, and mean of a set of data. First, let's consider the data from the Drama Club students. There are 9 students aged 15, 7 students aged 16, 11 students aged 17, and 4 students aged 18.
The mode is the value that appears most frequently in a data set. In this case, the age that appears most frequently is 17, because there are 11 students of that age. So, the first statement, 'The mode is 17,' is true.
The median is the middle value when the data set is ordered from least to greatest. Since there are 31 students in total (9 + 7 + 11 + 4), the median will be the age of the 16th student when the ages are listed in order. Listing them out, we will have nine 15-year-olds, seven 16-year-olds after that (making 16 so far), and then the 17-year-olds. So, the age of the 16th student is 16, making the median 16. The second statement, 'The median is 16,' is also true.
To calculate the mean, we add up all the ages and divide by the number of students. (9*15 + 7*16 + 11*17 + 4*18) / 31 = (135 + 112 + 187 + 72) / 31 = 506 / 31 ≈ 16.3. The mean age of the students is approximately 16.3 but not 15. Therefore, the third statement, 'The mean is 15,' is false.