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What is an advantage of using a stem-and-leaf plot instead of a histogram? What is the disadvantage?

This question aims to resolve the advantages and disadvantages of using a stem-and-leaf plot for visualizing statistical data.

Stem-and-leaf plots are used widely in visualizing the overall summary of statistical data. To develop an understanding of the core concept let’s consider the following arbitrary data as an example:

{ 1, 2, 3, 4, 5, 11, 12, 33, 44, 45, 44, 42, 41, 51, 51, 52, 53, 54, 55, 56, 57, 58, 59 }

Now if we consider a bin size of 10, we can tabulate this data against respective bins as follows:

\[ \begin{array}{ c | l } \text{ Stem } &  \text{ Leaves } \\———— & ———————————— \\ 00 \ – \ 09 & 1, 2, 3, 4, 5 \\ 10 \ – \ 19  & 11, 12 \\ 20 \ – \ 29 & 0 \\ 30 \ – \ 39 & 33 \\ 40 \ – \ 49 & 44, 45, 44, 42, 41 \\ 50 \ – \ 59 & 51, 51, 52, 53, 54, 55, 56, 57, 58, 59 \end{array} \]

\[ \text{ Table 1: Stem-and-leaf Plot of Some Arbitrary Data } \]

This simple plot that lists the number of elements in the data against each bin is referred to as the stem-and-leaf plot. Here the bin size values can be referred to as a stem while the individual data points listed against each of them are called leaves.

It’s worthwhile to note that the key difference between a histogram and the stem-and-leaf plot is that the histogram only notes the frequency or quantity of the elements falling in a certain bin while the stem-and-leaf plot enlists all the individual entries against each bin.

Expert Answer

When compared with a histogram, a stem-and-leaf plot has the advantage that all the data point values are also available for analysis while in histograms this data is lost and only the frequency of occurrences per bin is retained.

The disadvantage however is that the stem-and-leaf plots are very difficult to manage for large datasets and it’s tedious / resource-consuming to calculate it for various bin sizes. Histograms on the other hand are very efficient in this area and are easily scalable.

Numerical Result

Advantage: Stem-and-leaf plots contain information against each data point against each bin.

Disadvantage: Stem-and-leaf plots are not efficiently scalable to large data.

Example

Draw the stem-and-leaf plot of the following data:

\[ \{ 11, 3, 33, 14, 25, 41, 52, 3, 34, 15, 54, 22, 21, 51, 11, 52, 58, 54, 16, 28, 7, 8, 39, 48 \} \]

Assume a bin size of 5.

The stem-and-leaf plot is given below:

\[ \begin{array}{ c | l } \text{ Stem } &  \text{ Leaves } \\ ———— & ——————– \\ 00 \ – \ 04 & 3, 3\\ 05 \ – \ 09 & 7, 8 \\ 10 \ – \ 14 & 11, 14, 11 \\ 15 \ – \ 19 & 15, 16 \\ 20 \ – \ 24 & 22, 21 \\ 25 \ – \ 29 & 25, 28 \\ 30 \ – \ 34 & 33, 34 \\ 35 \ – \ 39 & 39 \\ 40 \ – \ 44 & 41 \\ 45 \ – \ 49 & 48 \\ 50 \ – \ 54 & 52,  54, 51, 52, 54 \\ 55 \ – \ 59 & 58 \\ \end{array} \]

\[ \text{ Table 2: Stem-and-leaf Plot of Example Data } \]

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