Box Plot

What is Boxplot?

A box plot is a graphical summary of a dataset. It displays the minimum, first quartile, median, third quartile, and maximum values. The box represents the interquartile range (IQR), which contains the middle 50% of the data. The median divides the box into two halves. Whiskers extend from the box and indicate the range of non-outlier data. Outliers, if present, are represented as individual points or asterisks. Box plots provide a visual depiction of the distribution, skewness, and presence of outliers in a dataset. They are useful for comparing multiple datasets or analyzing the distribution of a single dataset.

When to use Boxplot?

Box plots are commonly used in data analysis and visualization for several purposes. Here are some situations where box plots are particularly useful:

  • Visualizing distribution: Box plots provide a clear and concise representation of the distribution of a dataset, including the central tendency and spread of the data. They can be used to quickly assess the skewness, symmetry, and presence of outliers in the data.
  • Comparing multiple groups: Box plots are effective for comparing the distributions of multiple groups or categories. By placing multiple box plots side by side, you can easily compare the medians, quartiles, and ranges of different datasets and identify any differences or similarities.
  • Identifying outliers: Box plots provide a visual indication of potential outliers in a dataset. Observations that fall significantly outside the whiskers are often considered outliers and may warrant further investigation.
  • Exploring relationships: Box plots can be used to explore the relationship between a numerical variable and a categorical variable. For example, you can create box plots to analyze how a continuous variable (e.g., income) varies across different categories (e.g., age groups or education levels).
  • Summarizing data: Box plots provide a concise summary of key statistics, such as quartiles, median, and outliers, in a single visual representation. They are particularly useful when you want to present a summary of the data without overwhelming the audience with detailed numerical values.

Guidelines for correct usage of Boxplot

  • Sample size should be at least 20 for an effective representation
  • Boxplots are ideal for sample sizes of 20 or more
  • If sample size is too small, boxplot may not show meaningful quartiles and outliers
  • For sample sizes less than 20, consider using an Individual value plot
  • Sample data should be selected randomly
  • Random samples are used to make inferences about a population
  • Non-random data collection may lead to results that don't represent the population.

Alternatives: When not to use Boxplot

  • Histograms: Histograms are better suited than boxplots when you need a more detailed view of the distribution, want to analyze specific intervals or ranges, detect multimodal patterns, deal with large datasets, or understand the skewness of the distribution.
  • Scatterplot: Scatter plots are better suited than boxplots when you need to analyze the relationship between two continuous variables, detect outliers, identify nonlinear relationships, reveal heteroscedasticity, or detect clustering patterns in the data.

Example of Boxplot?

The goal of a plant fertilizer manufacturer is to develop a fertilizer formula that maximizes plant height growth. In order to test different fertilizer formulas, a scientist sets up three sets of 50 identical seedlings. These sets include a control group with no fertilizer, a group treated with the manufacturer's fertilizer called GrowFast, and a group treated with a competitor's fertilizer called SuperPlant. After being placed in a controlled greenhouse environment for three months, the scientist measures the heights of the plants.

As part of the initial investigation, the scientist constructs a boxplot representing the plant heights from the three groups. This boxplot is used to assess the variations in plant growth between the group without any fertilizer, the group treated with the manufacturer's fertilizer, and the group treated with the competitor's fertilizer. She has performed this in following steps:

  1. She worked all day and gathered the necessary data.
  2. Now, she analyzes the data with the help of https://qtools.zometric.com/
  3. Inside the tool, she feeds the data along with other inputs as follows:
  4. After using the above mentioned tool, she fetches the output as follows:

How to do Boxplot

The guide is as follows:

  1. Login in to QTools account with the help of https://qtools.zometric.com/
  2. On the home page, you can see Boxplot under Graphical Analysis.
  3. Click on Boxplot and reach the dashboard.
  4. Next, update the data manually or can completely copy (Ctrl+C) the data from excel sheet and paste (Ctrl+V) it here.
  5. Next, you need to map the columns with the parameters.
  6. Finally, click on calculate at the bottom of the page and you will get desired results.

On the dashboard of Boxplot, the window is separated into two parts.

On the left part, Data Pane is present. In the Data Pane, each row makes one subgroup. Data can be fed manually or the one can completely copy (Ctrl+C) the data from excel sheet and paste (Ctrl+V) it here.

On the right part, there are many options present as follows:

  • Orientation: In a boxplot, the term "orientation" refers to the direction in which the boxplot is displayed on a graph:
    • Horizontal Orientation: In this orientation, the boxplot is displayed horizontally, with the line or box representing the median and quartiles extending along the x-axis. The whiskers, which indicate the range of the data, also extend horizontally. This orientation is often used when the labels or categories on the x-axis are long or when comparing multiple boxplots side by side.
    • Vertical Orientation: In this orientation, the boxplot is displayed vertically, with the line or box representing the median and quartiles extending along the y-axis. The whiskers also extend vertically. This is the most common orientation for boxplots and is often used to compare the distributions of different variables or groups.
  • Boxmode: "Boxmode" in boxplot refers to the way the boxes are displayed in a boxplot when there are multiple boxes or datasets being compared in the same plot. When there are multiple boxes in a boxplot, the boxes can be displayed in different modes:
    • Group Mode: In this mode, the boxes are displayed next to each other, with a small gap between them. Each box represents a different group or category in the data, and this mode is useful for comparing the distributions of different groups.
    • Overlay Mode: In this mode, the boxes are overlaid on top of each other, so that only the median line and whiskers are visible. This mode is useful when the distributions of the groups are similar or when comparing the overall spread of the data.