1. What is a Box Plot?

A box plot (or 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, third quartile (Q3), and maximum. It shows outliers and what the values are, how the values are clustered, and if they are symmetrical or not.

2. How to Use This Calculator

Simply enter the five-number summary values (minimum, Q1, median, Q3, maximum) and click "Generate Box Plot". You can optionally add a title for your plot.

3. Understanding Box Plot Components

• Minimum: The smallest number in the dataset (excluding outliers)
• First Quartile (Q1): 25th percentile - 25% of data falls below this value
• Median: 50th percentile - middle value of the dataset
• Third Quartile (Q3): 75th percentile - 75% of data falls below this value
• Maximum: The largest number in the dataset (excluding outliers)
• Whiskers: Lines extending from the box to the minimum and maximum
• Box: Represents the interquartile range (IQR) between Q1 and Q3

4. Applications of Box Plots

Box plots are useful for:

• Comparing distributions between multiple groups
• Identifying outliers in the data
• Showing the skewness of the data distribution
• Displaying the spread and central tendency of data

5. Frequently Asked Questions (FAQ)

Q1: What if my values aren't in order (min ≤ Q1 ≤ median ≤ Q3 ≤ max)?
A: The calculator will not generate a plot if the values are not in the correct order, as this would represent invalid statistics.

Q2: How is the interquartile range (IQR) calculated?
A: IQR = Q3 - Q1. This represents the middle 50% of the data.

Q3: What are outliers in a box plot?
A: Outliers are typically defined as values that fall below Q1 - 1.5×IQR or above Q3 + 1.5×IQR.

Q4: When should I use a box plot vs. a histogram?
A: Use box plots for comparing distributions between groups and histograms for showing the shape of a single distribution.

Q5: Can I add multiple box plots to compare groups?
A: This calculator shows one box plot at a time, but you could generate multiple plots for comparison.