Final answer:
To answer the student's question, we arranged the data set, calculated the mean, identified the median, determined the modes, and found the range, resulting in a mean of 29.67, a median of 34, modes of 22 and 34, and a range of 47.
Step-by-step explanation:
To find the mean, median, mode, and range of the given data set (35, 8, 12, 50, 55, 22, 34, 22, 34), we must first organize the data in ascending order.
Arrange the data: 8, 12, 22, 22, 34, 34, 35, 50, 55.
Calculate the mean (average): (8 + 12 + 22 + 22 + 34 + 34 + 35 + 50 + 55) / 9 = 29.67.
Identify the median (middle value): There are 9 numbers, so the median is the 5th number, which is 34.
Determine the mode (most frequent value): Both 22 and 34 appear twice, making them the modes. This data set is bimodal.
Find the range (difference between the highest and lowest values): 55 - 8 = 47.
The data set's mean is 29.67, the median is 34, it has two modes 22 and 34, and the range is 47.