The main reason to use a stem-and-leaf plot instead of a dot plot is to assess group trends and individual values better. Both are methods of grouping data and can be used to recognize trends in that data, and some trends are more obvious in one or the other.
Dot plots and stem-and-leaf plots look and behave similarly. They have a list of increasing values or groups of values on one side of a line, and on the other side of the line, they mark how often those values occur. Usually, dot plots are easier to make, but stem-and-leaf plots give more information in some cases.
Dot plots usually list the values or intervals horizontally and stack "X"s above each interval to tally their frequency. Stem-and-leaf plots list intervals, often the largest relevant digit, vertically and place the lower-value digits to their right.
Both could be used to analyze a string of numbers, such as "17, 22, 23, 22, 16, 21, 18, 20, 20, 22, 17, 25, 19, 22, 17."
In the dot plot, all whole numbers between 16 and 25 could be listed, and each value would be marked for the number of times that it occurs. This makes finding the mode very easy.
In the stem-and-leaf plot, 10s digits 1 and 2 would create two rows. The ones digits that correspond to that 10 would follow in order to the right of the line. In this case, an analyst could see grouping and still be able to locate median and mode.