The Box and Whisker Plot, also known as the box plot, is a graphical representation of statistical data that was first introduced by John Wilder Tukey in 1969. Tukey was an American statistician and mathematician who made significant contributions to the field of statistics, particularly in the areas of data visualization and exploratory data analysis.
The box plot was designed as a way to quickly and easily represent the distribution of a dataset, and to identify potential outliers. It is particularly useful for comparing the distribution of multiple sets of data. The plot consists of a box that represents the middle 50% of the data, with a line inside the box representing the median. The box is also divided by a horizontal line, called the “whisker,” which represents the minimum and maximum values of the data. Any data points outside of this range are considered outliers and are represented by individual dots.
To construct a box plot, the first step is to find the minimum and maximum values of the data. Next, the median and the first and third quartiles are calculated. The median is the middle value of the data, and the quartiles are values that divide the data into four equal parts. Once these values are found, the box is drawn to represent the first and third quartiles, with the median line inside the box. The whiskers are then added to represent the minimum and maximum values, and any outliers are represented by individual dots.
The box plot quickly became a popular way to represent statistical data, and it is still widely used today in fields such as finance, engineering, and medicine. It is particularly useful for comparing the distribution of multiple sets of data, as it allows for easy visual comparison of the median, quartiles, and outliers.
Tukey’s box plot also paved the way for other forms of data visualization such as violin plot, bean plot, and letter-value plot. These plots also provide similar information as box plot but in a different way with variations.
To create a box and whisker plot, the first step is to find the median of the data set, which is the middle value when the data is arranged in numerical order. Next, the lower quartile, or Q1, is found, which is the value that separates the lowest 25% of the data from the rest. The upper quartile, or Q3, is also found, which is the value that separates the highest 25% of the data from the rest.
Once the median, Q1, and Q3 have been found, a box is drawn between Q1 and Q3 to represent the middle 50% of the data. A line is then drawn through the box to represent the median. Whiskers are then added to the plot, extending from the box to the minimum and maximum values of the data set. Any data points outside of the whiskers are considered outliers and are represented by individual dots on the plot.
Example 1: A teacher wants to compare the test scores of two classes. The first class had a median score of 80, Q1 of 75, and Q3 of 85. The second class had a median score of 90, Q1 of 85, and Q3 of 95. The box and whisker plot would show that the second class had a higher median and a higher range of scores than the first class.
Example 2: A company wants to compare the salaries of its employees. The median salary is $60,000, Q1 is $55,000, and Q3 is $65,000. The box and whisker plot would show that the majority of the employees make between $55,000 and $65,000 and that the median salary is $60,000.
Example 3: A researcher wants to study the weight of a certain type of fish. The median weight is 5 pounds, Q1 is 4 pounds, and Q3 is 6 pounds. The box and whisker plot would show that the majority of the fish weigh between 4 and 6 pounds and that the median weight is 5 pounds.
Example 4: A doctor wants to study the blood pressure of his patients. The median blood pressure is 120/80, Q1 is 110/70, and Q3 is 130/90. The box and whisker plot would show that the majority of the patients have a blood pressure between 110/70 and 130/90 and that the median blood pressure is 120/80.
Example 5: A real estate agent wants to compare the prices of houses in two different neighborhoods. The median price in the first neighborhood is $300,000, Q1 is $280,000, and Q3 is $320,000. The median price in the second neighborhood is $450,000, Q1 is $400,000, and Q3 is $500,000. The box and whisker plot would show that the houses in the second neighborhood are generally more expensive than those in the first neighborhood.
Quiz:
- What is a box and whisker plot?
- How is the median of a data set found?
- What does Q1 represent in a box and whisker plot?
- What does Q3 represent in a box and whisker plot?
- What is the purpose of whiskers in a box and whisker plot?
- How are outliers represented on a box and whisker plot?
