How to Create A Box Plot Without Outliers on Calculate

What is a Box Plot?

A box plot, 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 box plot consists of:

• The box itself, which represents the interquartile range (IQR) from Q1 to Q3
• A line inside the box showing the median
• Whiskers extending from the box to the minimum and maximum values
• Potential outlier points beyond the whiskers

Box plots are particularly useful for comparing distributions between different groups or for identifying outliers in a dataset.

Why Remove Outliers?

Outliers can significantly affect the interpretation of your data. Removing them can provide a clearer picture of the typical range of your data and help you focus on the central tendency rather than extreme values.

Reasons to remove outliers include:

• Improving the accuracy of statistical measures like mean and standard deviation
• Making the data distribution more representative of the typical cases
• Reducing the impact of measurement errors or exceptional cases
• Creating more comparable box plots when dealing with multiple datasets

Steps to Create a Box Plot Without Outliers

1. Collect and Organize Your Data

   Gather your dataset and sort the values in ascending order. This will help you identify the quartiles and outliers more easily.

2. Calculate the Five-Number Summary

   Calculate the minimum, Q1, median (Q2), Q3, and maximum values of your dataset.

   Formula:

   • Minimum: Smallest value in the dataset
   • Q1: Median of the first half of the data
   • Median (Q2): Middle value of the entire dataset
   • Q3: Median of the second half of the data
   • Maximum: Largest value in the dataset

3. Identify and Remove Outliers

   Use the IQR method to identify outliers. Values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR are considered outliers.

   Outlier Formula:

   IQR = Q3 - Q1

   Lower bound = Q1 - 1.5 × IQR

   Upper bound = Q3 + 1.5 × IQR

   Remove these outliers from your dataset before creating the box plot.

4. Create the Box Plot

   Using your cleaned dataset (without outliers), create the box plot with:

   • A box from Q1 to Q3
   • A line at the median (Q2)
   • Whiskers extending to the minimum and maximum values

5. Interpret the Results

   Analyze the box plot to understand the distribution of your data. Look at the spread, skewness, and any remaining outliers.

Formula Used

The key formulas for creating a box plot without outliers are:

Worked Example

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

1. Sort the Data

   5, 7, 8, 10, 12, 14, 15, 16, 20, 22, 25, 30, 50

2. Calculate Five-Number Summary

   • Minimum: 5
   • Q1: Median of first half (5,7,8,10,12,14) = 9.5
   • Median (Q2): Middle value (15)
   • Q3: Median of second half (16,20,22,25,30,50) = 26.5
   • Maximum: 50

3. Identify Outliers

   IQR = 26.5 - 9.5 = 17

   Lower bound = 9.5 - 1.5×17 = 9.5 - 25.5 = -16

   Upper bound = 26.5 + 1.5×17 = 26.5 + 25.5 = 52

   Only 50 is above the upper bound (52), so it's an outlier.

4. Remove Outlier and Create Box Plot

   Remove 50 and create the box plot with the remaining data.

   The box plot will show:

   • Box from Q1 (9.5) to Q3 (26.5)
   • Median line at 15
   • Whiskers to minimum (5) and maximum (30)