# Dot plot

## What is a dot plot?

A dot plot is a type of graphic display which shows frequencies of data points. Each dot represents a value of numeric variable and they are placed in columns. Furthermore, each column represents (relative) frequency of observations in a certain category.

For example, Tom wanted to find out how many hours per night do his fellow students usually sleep. He asked $30$ students and got the following results:

$$5, 7, 6, 8, 10, 5, 6, 6, 7, 8, 7, 6, 5, 9, 8, 9, 6, 7, 8, 7, 5, 6, 7, 8, 8, 6, 5, 7, 7, 5.$$

After that, Tom drew a dot plot of the given results: In other words, Tom drew a number line which he labeled from $5$ to $10$, because that is the range of the collected data.

Remember that range of a data set is the difference between the maximum and minimum value.

After that he placed dots above written numbers in a way that each number from the data set was represented by a dot.

Therefore, $6$ students usually sleep $5$ hours per night, $7$ students $6$ hours per night and so on. Only $1$ student sleeps $10$ hours per night.

Tom concluded that most of his fellow students usually sleep $7$ hours per night. Precisely, $8$ students sleep $7$ hours per night.

If a particular value doesn’t appear in a given data set, we still must write it in the number line (of course, if the value is in the given range). For instance, if the given data set is $\{1, 2, 3, 5, 7, 9, 10\}$, numbers $4, 6$ and $8$ must be included in the number line.

## Examples

Example 1:  Mark participates in a chess tournament. The following data points represent how many games he won in each tournament:

$$1, 2, 2, 0, 3, 4, 6, 2, 4, 2 .$$

Create a dot plot where each dot represents a number of games that Mark won.

Solution:

The minimum value of given data set is number $0$ and the maximum value is number $6$. Therefore, we need to label the number line from $0$ to $6$. Of course, we also must include number $5$ in the number line. Example 2:  An owner of a pancake bar wanted to see which pancake add – ins are most popular. Suppose $50$ people were asked to choose their favorite add – in. The results are: Create a dot plot where each dot represents how many people prefer a specific add – in.

Which add – in is most popular and which the least? Is strawberry syrup more popular than yoghurt?

Solution: The most popular add – in is chocolate and the least popular is cinnamon. Strawberry syrup is as popular as yoghurt.

Example 3: A sample of $10$ students was asked how many brothers and sisters they have.  The results are in the following table: Create a dot plot. Which is the most common number of brothers and sisters?

Solution:

The minimum value of given data set is number $0$ and the maximum value is number $3$. Therefore, we need to label the number line from $0$ to $3$. The most common number of brothers and sisters is $1$.

As we can see in the examples above, we use this type of graphic display in situations when data sets are relatively small.