91Ó°ÊÓ

A dot plot is one of the simplest ways to visualize data, where each data point is represented by a dot on a number line. It's especially useful for small data sets because it shows every individual value.
In making a dot plot, each value from the data set is plotted as a dot above a number line that corresponds to that value. For example, if you have values like 15, 9, and 5, you place a dot above 15, another above 9, and another above 5 on the number line.
Dot plots offer several advantages:

• They display clusters of data points.
• They show all individual values in the data set.
• They provide a clear visual representation of data distribution.

However, while dot plots are highly detailed, they can become cluttered with large data sets which might make it difficult to interpret at a glance.

A box plot, also known as a whisker plot, provides a graphical summary of a data set's central tendency, dispersion and skewness. It consists of a rectangular "box", lines known as "whiskers", and often individual outliers.
A box plot is constructed using the following elements:

• The "box" spans from the first quartile (Q1) to the third quartile (Q3), encompassing the middle 50% of the data.
• A line inside the box indicates the median of the data set.
• Whiskers extend from the box to the minimum and maximum data values, showing the range of the data.

Box plots are particularly useful in identifying the skewness of data and any potential outliers. For example, if the median is closer to one side of the box, it can indicate the data is skewed.
While a box plot does a great job summarizing data, it doesn't clearly show the details like clusters or gaps in the data that a dot plot might reveal. This is why combining different types of plots can provide comprehensive insights into the data.

Quartiles are values that divide a data set into four equal parts, helping to describe the spread and center of the data distribution. Calculating quartiles involves ordering your data and finding specific points in the data set:

• The first quartile (Q1) is the median of the lower half of the data. This is the 25th percentile, which means 25% of the data falls below this point.
• The second quartile (Q2) is the median, cutting the data set in half.
• The third quartile (Q3) is the median of the upper half, representing the 75th percentile, where 75% of the data lies below it.

As seen in our example: Q1 was 9, meaning a quarter of the stock prices were under $9. Q3 was 39, indicating three-quarters of the prices were less than $39. The interquartile range (IQR), Q3 minus Q1, shows the spread of the central 50% of the data, offering insights into data variability.
This way, quartiles help to quickly understand data distribution and are vital components of a box plot, contributing to its ability to summarize data visually.

A stem-and-leaf plot is a method of displaying quantitative data that retains the actual data values while also giving a visual sense of the data's distribution. It's like a histogram turned sideways. Each data point is split into a "stem" and "leaf":

• The "stem" includes all but the last digit of a number. For instance, for 15, the stem is 1.
• The "leaf" is the final digit of the number. So for 15, the leaf is 5.

In this plot, stems are listed in increasing order along a column, and leaves are added in rows corresponding to each stem.
This plot has its advantages:

• It maintains the original data values, allowing you to see precise figures within the context of overall distribution.
• It quickly highlights gaps, clusters, and outliers.
• It combines the functionality of a table and a graph.

Stem-and-leaf plots are especially useful for medium-sized data sets, providing a balance between detail and visual simplicity. They can easily show the shape of the data distribution, such as whether it is skewed or symmetrical, which is slightly less visible in box plots alone.