To find the mean, mode, median, and range of a data set, we first need to organize the data in numerical order. This will allow us to easily identify the middle value (median), the most common value (mode), and the range of the data. In this case, the data set in numerical order is:

5; 5; 6; 7; 9; 10; 17; 19; 21; 22; 24

The mean is calculated by adding all the values in the data set and dividing by the total number of values. In this case, the mean is calculated as follows: (5 + 5 + 6 + 7 + 9 + 10 + 17 + 19 + 21 + 22 + 24) / 11 = 125 / 11 = 11.363636

The mode is the value that appears most often in the data set. In this case, the mode is 5, because it appears twice, which is more than any other value.

The median is the middle value in the data set. In this case, there are 11 values in the data set, which means that the 6th and 7th values (9 and 10) are the middle values. Since there are two middle values, we need to find the mean of these two values to find the median. In this case, the median is (9 + 10) / 2 = 9.5

The range is the difference between the largest and smallest values in the data set. In this case, the range is 24 - 5 = 19.

Therefore, the mean, mode, median, and range of the data set are 11.363636, 5, 9.5, and 19, respectively.