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# Dot Plot|Definition & Meaning

## Definition

A **dot plot,** also known as a **strip** **plot,** is a **graphing method** that uses **dots** with an x and y-axis. These charts identify different **trends** and **group data** for ease of **interpretation.** Furthermore, the dot plots are similar to a **histogram,** as it shows a **distribution** of a set of data by showing the number of dots that **fall** into **each category.**

Moreover, the dot plots are considered one of the **simplest statistical graphs** to identify **clusters** and highlight **gaps** and **skews** in the **distribution.** Additionally, these dot plots are effective for a dataset of **less** than **20 to 30 variables**, as it is **less manageable** for a dot plot to depict a data set of more than 30 variables.

For a **higher number** dataset, one can **utilize** the **histogram** since it is difficult to manage and draw a **large quantity** of the dataset on the dot plot. This way, it is further emphasized to draw a **smaller dataset** on a dot plot since it is easier and takes less time to **analyze** and see the **general trend** of the **data samples.**

## Classification of Dot Plots

Dot plots are classified into **two types:**

**Wilkinson dot plot****Cleveland dot plot**

Given ahead is the **description** of these two types of dot plots, which both use dots, but one uses it in the sense of a **bar graph** while the other utilizes it as more of a **histogram.** Both of these dot plot types are widely used in statistics to analyze and **interpret implicit meaning** from the dataset.

### Wilkinson Dot Plot

**Wilkinson’s dot plot** was created by **Leland Wilkinson,** who devised this method to **ease** the **analysis** of dot plots and depict them as a **histogram.** These dot plots are the **standardized forms** of dot plots used in statistics. It represents the distribution of continuous dataset points, similar to a histogram, and hence, is widely used in **statistics.**

Thus, if we need to depict a **room’s temperature** for 24 hours per hour, we could use the dataset to write **continuous** data and draw them on the Wilkinson dot plot for ease of interpretation.

Let us take an example of twelve people taking part in **four sports: Badminton, Table Tennis, Football,** and **Cricket.** We have **three** people participating in badminton, **five** in Table tennis, **two** in Football and **two** in Cricket. The dot plot can be, thus, drawn as shown in **Figure** **2**.

Thus, with this **example,** we can see how the Wilkinson Dot plot is utilized to interpret the dataset provided by data **sampling** and finding the trend of the **overall data** from the dot plot.

### Cleveland Dot Plots

The **Cleveland dot plot** was created by **William S. Cleveland**, in an attempt to **reduce** **dot clusters** and **grouping** that might **hinder** the interpretation of a large dataset on the graph. These dot plots are similar to bar graphs, but instead of the length of the bar graph to depict the data of a particular label, the Cleveland dot plot uses the dot’s position on the graph to show the value of the data.

Cleveland dot plot is very useful when using **multiple variables** as it does not require starting from the **zero axis.** Instead of having all the dots, we can use only **one dot** and its location on the **y-axis** will depict the **value** of the dot.

## Examples Representing the Usage of Dot Plots

### Example 1

Given is the raw data of **time taken** for a task to be completed by **twenty students** in minutes: **5, 8, 3, 4, 9, 2, 4, 5, 3, 8, 5, 6, 7, 8, 9, 4, 8, 6, 5, 3**. From this dataset provided, draw a **Wilkinson’s** **dot plot** and find the **mean value** of the time taken for the task to be completed by twenty people. What is the **most common time value** for which the task was done and **by how many people** was this task done at that time?

### Solution

Given below is the dot plot drawn from the dataset given in the Example problem.

Hence, we can see that about **four** people have taken **five** and **eight minutes** to complete the task and so the most **common** time in minutes for completing the task is five and eight minutes by four people.

Now, to find the **mean value** of the **twenty people** to complete the task in minutes by taking the **weighted sum** of all the grouped data and dividing it by the total number of samples, that is, twenty.

\[ \text{Mean = } \frac{\sum^{9}_{i=2} x_i \times k_1}{n} \]

\[\text{Mean = } \frac{2 \times 1 + 3 \times 3 + 4\times 3 + 5 \times 4 + 6 \times 2 + 7 \times 1 + 8\times 4 + 9 \times 2}{20} \]

\[\text{Mean = } \frac{112}{20} \]

\[\text{Mean = } 5.6 \text{ minutes} \]

Thus the **mean time taken** for the task to complete is equal to **5.6 minutes.**

### Example 2

For the **dataset** of example 1, find the **standard deviation** of the time taken by the workers to complete a specific task.

### Solution

From Example 1, we found that the **mean** value of the time taken for the task is** 5.6 minutes.** To find the **standard deviation,** the following steps are taken to calculate it.

\[ \text{Squared Sum = } (2^2 \times 1) + (3^2 \times 3) + (4^2 \times 3)\]

\[+ (5^2 \times 4) + (6^2 \times 2) + (7^2 \times 1) + (8^2 \times 4) + (9^2 \times 2) = 718\]

\[ \text{Mean of Squared Sum = } \frac{718}{20} = 35.9 \]

\[ \text{Standard Deviation = } \sqrt{ 35.9 – 5.6^2 } \]

\[ \text{Standard Deviation = } \sqrt{ 4.54} \]

\[ \text{Standard Deviation = } 2.13 \]

Hence the **Standard Deviation** of the data is equal to **2.13 minutes.**

*All drawings and mathematical graphs are made using GeoGebra.*