kvartiil

A quartile is a statistical measure used to divide a dataset into four equal parts, each representing 25% of the data. The concept is widely applied in descriptive statistics to summarize the distribution of values within a dataset, particularly for continuous or ordinal data. Quartiles help identify the spread and skewness of data, providing insights into central tendencies beyond the mean and median.

There are three primary quartiles: Q1 (the first quartile), Q2 (the second quartile, also known as the median), and Q3 (the third quartile). Q1 represents the 25th percentile, meaning 25% of the data falls below this value, while Q3 represents the 75th percentile, with 75% of the data below it. The interquartile range (IQR), calculated as Q3 minus Q1, measures the spread of the middle 50% of the data and is useful for identifying outliers or variability within a dataset.

Quartiles are particularly valuable in box-and-whisker plots (box plots), where they visually represent the distribution of data. The box in a box plot spans from Q1 to Q3, with a vertical line at Q2 (the median). Whiskers extend to the smallest and largest values within 1.5 times the IQR from Q1 and Q3, respectively, while outliers are plotted individually beyond this range.

Calculating quartiles depends on the dataset’s size and method used. Common approaches include the Tukey method, which excludes the median in odd-sized datasets, and the Moore and McCabe method, which includes it. Different methods may yield slightly different quartile values, but they generally provide a similar understanding of data distribution.

Quartiles are commonly used in fields such as economics, education, and healthcare to analyze income distribution, test score performance, and medical measurements. They are particularly useful when data contains extreme values or is skewed, as they are less sensitive to outliers than the mean.