1. What is Five Number Summary?

The five number summary is a descriptive statistics tool that provides a quick overview of a dataset. It consists of five values: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. These values are used to create box plots and understand the distribution of the data.

2. How Does the Calculator Work?

The calculator computes the five number summary and percentiles from your input data:

Where:

• Minimum — The smallest value in the dataset
• Q1 (First Quartile) — 25th percentile, median of lower half
• Median (Q2) — 50th percentile, middle value
• Q3 (Third Quartile) — 75th percentile, median of upper half
• Maximum — The largest value in the dataset

Explanation: The calculator first sorts the data, then calculates each component of the five number summary using linear interpolation for quartiles.

3. Importance of Five Number Summary

Details: The five number summary provides a comprehensive view of data distribution including center, spread, and skewness. It's particularly useful for identifying outliers and comparing distributions between different datasets.

4. Using the Calculator

Tips: Enter your numerical data separated by commas. The calculator will ignore non-numeric values. For best results, provide at least 5 data points.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between quartiles and percentiles?
A: Quartiles are specific percentiles - Q1 is the 25th percentile, median is 50th, Q3 is 75th. Percentiles divide data into 100 equal parts.

Q2: How is this related to box plots?
A: Box plots visually represent the five number summary, with the box showing Q1 to Q3, a line at median, and whiskers extending to min/max (or 1.5*IQR for outliers).

Q3: What if my data has outliers?
A: The five number summary helps identify outliers (values below Q1-1.5*IQR or above Q3+1.5*IQR). Consider examining outliers carefully.

Q4: How is this different from mean and standard deviation?
A: Mean and SD assume normal distribution. Five number summary is non-parametric and better for skewed data.

Q5: What is the interquartile range (IQR)?
A: IQR = Q3 - Q1, representing the middle 50% of data. It's a robust measure of spread less affected by outliers than range.