CandleFocus

Quartile

Candlefocus Editor
Quartiles are a type of percentile that divides a data set into four equal parts. They divide the ranked data into four equal parts, and each part is called a quartile. Various quartiles can be defined depending on the context, but most commonly quartiles divide data into four equal parts. Therefore, the lower quartile divides the data set at the 25th percentile, the median divides it at the 50th percentile, and the upper quartile divides it at the 75th percentile.

The quartiles of a dataset can be used to calculate the spread and variation of a variable. Variation can be measured using the range, variance, and standard deviation of a dataset. However these measures are highly sensitive to outliers, as a single outlier can skew them. As a result, quartiles can be used as a more robust measure of variation.

The interquartile range (IQR) is a measure of variability, which quantifies the difference between the upper quartile and the lower quartile in the dataset. It is calculated by subtracting the lower quartile from the upper quartile. It is a measure of how the central, middle values are spread out across the dataset, and can be used to compare data distributions within the same dataset or between two different datasets.

The quartiles of a dataset can be used to identify outliers. Outliers are values which are significantly higher or lower than the majority of the data, and therefore can have a disproportionate influence on the mean and standard deviation, compensating measures that are sensitive to outliers. The IQR is a more robust measure, especially when outliers are present. The interquartile range is calculated by subtracting the lower quartile from the upper quartile. Two common criteria for identifying outliers are values that are less than q1 - 1.5*IQR or greater than q3 + 1.5*IQR.

Quartiles can also be used to compare the quartiles of two different datasets. The quartiles of the datasets can be compared to determine if the spread of values are similar or different. The quartiles of a dataset can also be compared to the quartiles of a normal distribution to determine if the data is normally distributed.

In summary, quartiles are a type of percentile where a data set is divided into four equal parts. They can be used to calculate the interquartile range, which is a measure of variability around the median. Quartiles can also be used to identify outliers, and to compare the quartiles of different datasets to see if the data is distributed similarly. Quartiles are an essential part of any data analysis, and can provide valuable insights into a data set.

Glossary Index