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 **c****ore 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 **s****tem-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:

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

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