A histogram and a stem-and-leaf plot display data in similar ways. To find which of them is better when we have a large data set, let's analyze how each of them is built.
Histogram
A histogram shows frequencies of data values in intervals of equal sizes. The height of the bar shows the frequency of data in the corresponding interval.
A histogram only displays frequencies, we cannot find out about the raw data from a histogram.
Stem-and-Leaf Plot
A stem-and-leaf plot shows the data in numerical order and how it is distributed. It looks similar to a histogram but oriented in a vertical way. Let's recall how we can make one!
Each data value is split into a stem and a leaf.
The stem includes all but the last non-zero digit — zeros at the end of large numbers can be ignored as long as they are explained in a key.
The last non-zero digit will be the leaf, which is always a single digit.
Two columns are drawn and separated with a vertical line.
The left column contains the stems in numerical order.
The right column contains the leaves in numerical order.
All of the stems must be written once, even if they do not have leaves. A key can help explain what the stems and leaves represent — this includes information such as units or digit place values. Let's look at an example.
One important thing to keep in mind is that a stem-and-leaf plot must include every data values in the data set.
Conclusion
Now that we have described both data displays, we can make some conclusions about them when using a large data set.
Histogram
Stem-and-Leaf Plot
For a histogram, the size of the data set does not cause a problem because we can always find a suitable number of intervals.
For a stem-and-leaf plot, the stems might not necessarily become problematic. However, no matter what, there will be a lot of leaves.
Therefore, a histogram would be more appropriate for a large data set.
