a) To create a stem-and-leaf plot, we need to separate each number into a stem and a leaf. The stem is the digit(s) to the left of the rightmost digit, and the leaf is the rightmost digit. For example, 219 would have a stem of 21 and a leaf of 9. The stem-and-leaf plot for this data is:
```
15 | 1
17 | 0 0 1 4
18 | 2 4 5 6 6
19 | 3 4 5 6 7 9
```
b) To find the median, we need to put the data in order from least to greatest:
```
151 170 170 171 174 178 179 182 184 185 186 186 186 193 194 195 196 197 199 219
```
There are 20 numbers in the data set, so the median is the average of the 10th and 11th numbers:
```
Median = (185 + 186) / 2 = 185.5
```
To find the mode, we look for the most common value in the data set. In this case, the stem-and-leaf plot shows that there are two modes: 186 and 170.
c) To calculate the mean, we add up all the numbers and divide by the total number of numbers:
```
Mean = (219 + 151 + 199 + 186 + 170 + 186 + 194 + 184 + 196 + 185 + 174 + 186 + 197 + 170 + 178 + 179 + 182 + 193 + 195 + 171) / 20
Mean = 1849 / 20
Mean = 92.45
```
Therefore, the mean of the data is 92.45.