Box and Whisker Plot | Meaning, Uses and Example

What is Box and Whisker Plot?

Box and Whisker Plot is defined as a visual representation of the five-point summary. The Box and Whisker Plot is also called as Box Plot. It consists of a rectangular “box” and two “whiskers.” Box and Whisker Plot contains the following parts:

• Box: The box in the plot spans from the first quartile (Q₁) to the third quartile (Q₃). This box contains the middle 50% of the data and represents the interquartile range (IQR). The width of the box provides insights into the data’s spread.
• Whiskers: The whiskers extend from the minimum value to Q₁ and from Q₃ to the maximum value. They signify the range of the data, excluding potential outliers. The whiskers can vary in length, indicating the data’s skewness or symmetry.
• Median Line: A line within the box represents the median (Q₂). It divides the data into two halves, revealing the central tendency.
• Outliers: Individual data points lying beyond the whiskers are considered outliers and are often plotted as individual points.

What is a Five-Point Summary?

The five-point summary rundown comprises five key measurements: the base worth, the principal quartile (Q₁), the middle (Q₂), the third quartile (Q₃), and the greatest worth. These measurements partition a dataset into four similarly estimated parts, uncovering important data about the dataset’s focal inclination, spread, and skewness.

Uses of Box and Whisker Plot

1. Imagining Information Dispersion: Box plots are brilliant instruments for acquiring a visual comprehension of the circulation of a dataset. They give a speedy outline of the central tendency, spread, and state of the information dissemination, assisting with distinguishing whether the information is symmetric, slanted, or contains exceptions.

2. Contrasting Distributions: Box plots are valuable for looking at the circulations of different datasets one next to the other. This is especially important when you need to think about the qualities of various gatherings, populaces, or classes. For instance, Contrasting the grades of understudies from various schools or locales, examining the exhibition of different items or medicines in a review, etc.

3. Estimating Skewness: By looking at the box and whiskers’ general lengths and positions, an individual can evaluate the skewness of the information. A more drawn-out tail on one side of the box recommends skewness that way.

4. Information Investigation: Box plots can act as starting tools for information investigation. They give a compact rundown of a dataset’s key qualities, assisting with settling on the proper information investigation techniques or changes.

5. Statistical Analysis: Box plots are much of the time utilised close by measurable tests and investigations. They can assist with picturing the circulation of information before directing speculation testing or looking at the method for various gatherings.

6. Quality Control: In assembling and quality control processes, box plots are utilised to screen varieties in item determinations and distinguish imperfections or deviations from quality guidelines. They help recognise when an interaction is working inside satisfactory cutoff points or when it needs changes.

7. Navigation: Box plots furnish chiefs with an unmistakable and instinctive method for surveying information qualities. They are utilised in business, money, and medical care to go with informed choices given information synopses.

8. Risk Appraisal: In fields like finance and insurance, box plots can be utilised to envision the gamble related to various speculations or protection contracts. They assist partners with figuring out the possible fluctuation in returns or misfortunes.

9. General Wellbeing and Epidemiology: Box plots are utilised to imagine and think about well-being-related information. For example, the circulation of illness rates among various districts or segment gatherings.

10. Ecological Sciences: Box plots can be applied to examine natural information. For example, air quality estimations or water contamination levels, and survey varieties across time or areas.

When to Use Box and Whisker Plot

Box and Whisker Plots are particularly useful in the following situations:

1. Comparing Scores: When there is a need to think about the performance of students from various classes or schools, a box plot can assist with surveying the dispersion of test scores in each gathering and recognise whether one gathering beats the others.

2. Analysing Worker Compensations: While examining the pay rates of representatives in an organisation, one can utilises box plots to look at the compensation circulations among various divisions or occupation jobs, assisting with recognising differences or exceptions.

3. Evaluating Product Quality: In assembling, if one needs to screen the nature of an item, one can make box plots of estimations taken at different creation runs. This recognises varieties and whether the item satisfies quality guidelines.

4. Distinguishing Anomalies in Financial Data: While examining monetary information, like stock returns, one can utilise box plots to identify exception exchanging days or uncommon cost developments, which might show huge occasions or blunders in information.

5. Comparing Patient Recuperation Times: In medical care, one could utilise box plots to think about the recuperation seasons of patients who have various therapies or medical procedures. This can assist with figuring out which treatment approach is more compelling.

6. Assessing Marketing Campaigns: Marketers can utilise box plots to evaluate the effect of various publicising efforts by contrasting measurements like navigate rates or change rates across crusade varieties.

7. Observing Air Quality: Ecological researchers and offices use box plots to envision air quality information, contrasting pollutant concentrations across various monitoring stations or locales.

8. Assessing Investment Portfolios: Financial experts can utilise box plots to think about the circulations of profits for various venture portfolios, assisting investors and backers with understanding gamble and return compromises.

9. Comparing Housing Prices: Real estate marketers can utilise box plots to think about the costs of houses in various areas or urban communities, giving experiences in real estate market varieties.

10. Breaking down Crime Percentages: Law enforcement agencies can utilise box plots to look at crime percentages in various regions or after some time, distribute assets and focus on mediations.

How to Make Box and Whisker Plot

The following steps are involved in making Box and Whisker Plot:

1. Gather Information: Accumulate the dataset of which the envision is needed.

2. Work out Quartiles: Track down the main quartile (Q₁), third quartile (Q₃), and median (Q₂) from the given information.

3. Decide Whiskers: Ascertain the base and most extreme qualities, barring anomalies.

4. Plot the Box and Whiskers: Draw a case from Q₁ to Q₃, a line inside the crate at Q₂, and hairs from the base to Q₁ and from Q₃ to the greatest.

5. Recognise Outliers: Plot any pieces of information outside the stubbles as individual focuses.

Example of Box and Whisker Plot

Example:

Suppose we have a dataset representing the test scores of a group of students: Data (test scores): 78, 85, 90, 92, 95, 96, 97, 98, 99, 100, 105, 110, 120.

Solution:

Step 1: Collect Data

Dataset: 78, 85, 90, 92, 95, 96, 97, 98, 99, 100, 105, 110, 120

Step 2: Calculate Quartiles

To create a Box and Whisker Plot, we need to calculate the quartiles (Q₁ and Q₃) and the median (Q₂).

-Q1 (the first quartile) is the median of the lower half of the data (78, 85, 90, 92, 95, 96) = 91

-Q2 (the median) is the median of the entire dataset = 97

-Q3 (the third quartile) is the median of the upper half of the data: (98, 99, 100, 105, 110, 120) = 102.5

Step 3: Determine Whiskers

To find the whiskers, calculate the minimum and maximum values within the dataset, excluding potential outliers.

Minimum = 78, Maximum = 120

The required five-number summary is 78, 91, 97, 102.5, 120.

Step 4: Plot the Box and Whiskers

Now, we can create the Box and Whisker Plot:

-Draw a box from Q₁ (91) to Q₃ (102.5).

-Draw a line inside the box at Q₂ (97).

-Extend the left whisker from the minimum (78) to Q₁ (91).

-Extend the right whisker from Q₃ (102.5) to the maximum (120).

Step 5: Identify Outliers

Any data points that fall outside the whiskers are considered outliers. In this case, we do not have any outliers. This Box and Whisker Plot gives a visual rundown of the grades, showing the middle (Q₂) at 97, the interquartile range (IQR) from Q₁ to Q₃ (91 to 102.5), and the shortfall of exceptions. It successfully outlines the focal propensity, spread, and dissemination of the dataset.