1. What is a Box and Whisker Plot?

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, third quartile (Q3), and maximum. It shows outliers and what the range of the data is.

2. How Does the Calculator Work?

The calculator computes the key values needed for a box and whisker plot:

Where:

• \( Q1 \) — First quartile (25th percentile)
• \( Q3 \) — Third quartile (75th percentile)
• Median — Middle value of the dataset
• IQR — Interquartile range (Q3 - Q1)
• Fences — Boundaries for outlier detection (1.5 × IQR from Q1 and Q3)

3. Understanding Quartiles

Details: Quartiles divide the data into four equal parts. The box in the plot represents the middle 50% of the data (between Q1 and Q3), while the whiskers typically show the range of the data (excluding outliers).

4. Using the Calculator

Tips: Enter your numerical data separated by commas or spaces. The calculator will sort the data and compute all necessary values for creating a box and whisker plot.

5. Frequently Asked Questions (FAQ)

Q1: What is the interquartile range (IQR)?
A: The IQR is the range between the first and third quartiles (Q3 - Q1). It represents the middle 50% of the data.

Q2: How are outliers determined?
A: Outliers are typically defined as values that fall below Q1 - 1.5×IQR or above Q3 + 1.5×IQR.

Q3: What if my dataset has an even number of values?
A: The median (and quartiles) will be calculated as the average of the two middle numbers in that case.

Q4: Can I use this for non-numerical data?
A: No, box and whisker plots are only meaningful for numerical data that can be ordered.

Q5: How should I interpret a box plot?
A: The box shows the middle 50% of data, the line in the box is the median, and the whiskers show the range. Points outside the whiskers are outliers.