What is the five number summary in statistics?

The five number summary consists of: minimum (smallest value), Q1 (first quartile, 25th percentile), median (second quartile, 50th percentile), Q3 (third quartile, 75th percentile), and maximum (largest value). These five values provide a comprehensive view of your data's distribution and spread.

How are quartiles different from percentiles?

Quartiles divide data into four equal parts, while percentiles divide into 100 parts. Quartiles are specific percentiles: Q1 is the 25th percentile, Q2 (median) is the 50th percentile, and Q3 is the 75th percentile. Quartiles are commonly used because they efficiently summarize data distribution without overwhelming detail.

What is the interquartile range (IQR)?

IQR is Q3 minus Q1, representing the middle 50% of your data. IQR = Q3 - Q1. It's a robust measure of spread that isn't affected by extreme outliers, unlike range (max - min). IQR is used to identify outliers: values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR are considered potential outliers.

How do I calculate quartiles for my dataset?

First, sort your data in ascending order. The median divides the dataset in half. Q1 is the median of the lower half (below the median), and Q3 is the median of the upper half (above the median). Methods vary slightly depending on whether you include or exclude the median itself when you have an odd number of values.

What is a box plot and how does it use the five number summary?

A box plot (box-and-whisker plot) visualizes the five number summary. The box spans from Q1 to Q3 (showing the IQR), with a line at the median. Whiskers extend to the minimum and maximum (or to a calculated limit, with outliers shown as individual points). Box plots make it easy to see distribution shape, center, and spread at a glance.