Statistics made easy - 9 - Quartiles, Percentiles and Range - Box plot and five point summary
Quartiles: Quartiles are values that divide a dataset into four equal parts. The first quartile (Q1) is the value below which 25% of the data falls, the second quartile (Q2) is the median (50th percentile), and the third quartile (Q3) is the value below which 75% of the data falls.
Percentiles: Percentiles are similar to quartiles but divide the data into 100 equal parts. The nth percentile is the value below which n% of the data falls.
Range: The range of a dataset is the difference between the maximum and minimum values. It gives a measure of the spread of the data.
Interquartile Range (IQR): The interquartile range is a measure of statistical dispersion, which is calculated as the difference between the third quartile (Q3) and the first quartile (Q1), giving a measure of the spread of the middle 50% of the dataset.
Five-Number Summary: The five-number summary consists of five values: the minimum, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum. It provides a concise summary of the distribution of the dataset.
Box Plot (Box-and-Whisker Plot): A box plot is a graphical representation of the five-number summary. It consists of a box, which spans from the first quartile (Q1) to the third quartile (Q3), with a line representing the median (Q2). Whiskers extend from the box to the minimum and maximum values or a specified range, and outliers may be represented as individual points.
These statistical tools are useful for summarizing and visualizing the distribution of data, providing insights into central tendency, spread, and the presence of outliers. They are commonly used in exploratory data analysis and descriptive statistics.