How to Create A Boxplot Without Outliers on Calculator

What is a Boxplot?

A boxplot, also known as a box-and-whisker plot, is a standardized way of displaying the distribution of data based on a five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. The boxplot provides a visual summary of the data's central tendency, variability, and skewness.

The components of a boxplot include:

• Box: Represents the interquartile range (IQR), which is the range between Q1 and Q3. The box contains the middle 50% of the data.
• Median line: A line inside the box that shows the median (Q2) of the data.
• Whiskers: Lines extending from the box that show the range of the data, typically from the minimum to the maximum values.
• Outliers: Data points that fall outside the whiskers and are considered unusual or extreme values.

Why Remove Outliers?

Outliers can significantly affect the interpretation of a boxplot by skewing the representation of the data's central tendency and spread. Removing outliers helps to:

• Provide a clearer view of the typical range of the data.
• Reduce the impact of extreme values on the analysis.
• Improve the readability of the boxplot by focusing on the main distribution of the data.

However, it's important to consider why outliers exist and whether they should be removed or investigated further.

How to Create a Boxplot Without Outliers

Creating a boxplot without outliers involves the following steps:

1. Collect and organize your data: Ensure you have a dataset with numerical values that you want to visualize.
2. Calculate the five-number summary: Compute the minimum, Q1, median, Q3, and maximum values of your dataset.
3. Identify and remove outliers: Determine which data points are outliers and exclude them from the boxplot.
4. Create the boxplot: Use the cleaned dataset to create the boxplot.

Step 1: Calculate the Five-Number Summary

The five-number summary consists of:

• Minimum: The smallest value in the dataset.
• Q1 (First Quartile): The value below which 25% of the data falls.
• Median (Q2): The middle value of the dataset.
• Q3 (Third Quartile): The value below which 75% of the data falls.
• Maximum: The largest value in the dataset.

Step 2: Identify and Remove Outliers

Outliers are typically defined as data points that fall below Q1 - 1.5 × IQR or above Q3 + 1.5 × IQR, where IQR is the interquartile range (Q3 - Q1).

Any data points outside these bounds are considered outliers and should be removed before creating the boxplot.

Step 3: Create the Boxplot

With the cleaned dataset, you can create the boxplot using the five-number summary. The boxplot will now represent the distribution of the data without the influence of outliers.

Worked Example

Let's create a boxplot without outliers for the following dataset: 5, 7, 8, 10, 12, 14, 15, 16, 20, 22, 25, 30, 50.

Step 1: Calculate the Five-Number Summary

• Minimum: 5
• Q1: 10 (median of the first half of the data)
• Median (Q2): 15 (middle value of the dataset)
• Q3: 20 (median of the second half of the data)
• Maximum: 50

Step 2: Identify and Remove Outliers

Calculate the IQR and the outlier bounds:

• IQR: Q3 - Q1 = 20 - 10 = 10
• Lower Bound: Q1 - 1.5 × IQR = 10 - 1.5 × 10 = -5
• Upper Bound: Q3 + 1.5 × IQR = 20 + 1.5 × 10 = 35

The value 50 is above the upper bound (35), so it is considered an outlier and should be removed.

Step 3: Create the Boxplot

Using the cleaned dataset (5, 7, 8, 10, 12, 14, 15, 16, 20, 22, 25, 30), create the boxplot with the following five-number summary:

• Minimum: 5
• Q1: 10
• Median (Q2): 15
• Q3: 20
• Maximum: 30

The resulting boxplot will provide a clearer view of the central tendency and spread of the data without the influence of the outlier (50).