Interquartile range
Definition
The Interquartile Range (IQR) is a statistical measure used to represent the middle spread of data. It is a measure of statistical dispersion, or how far apart numbers in a data set are. The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). This range includes the middle 50% of the data, thus providing a measure of where the bulk of the values lie.
Calculation
The calculation of the IQR involves several steps. First, the data set must be ordered from least to greatest. Then, the median of the data set is found. The median divides the data set into two halves. The lower half is used to find Q1, the median of the lower half of the data. Similarly, Q3 is found by calculating the median of the upper half of the data. The IQR is then calculated by subtracting Q1 from Q3.
Use in Data Analysis
The IQR is a valuable tool in data analysis. It provides a measure of how spread out the middle values in a data set are. This can be useful in identifying outliers, as any data point that falls below Q1 - 1.5*IQR or above Q3 + 1.5*IQR is considered an outlier. The IQR is also used in the creation of box plots, a type of graph used to display the distribution of data.
Comparison with Other Measures of Dispersion
The IQR is one of several measures of dispersion, including the range, variance, and standard deviation. Unlike these other measures, the IQR is not affected by extreme values, as it only considers the middle 50% of the data. This makes it a more robust measure of dispersion, particularly for data sets with outliers or non-normal distributions.
Limitations
While the IQR is a useful measure of dispersion, it does have some limitations. It does not provide information about the shape of the distribution, such as skewness or kurtosis. Additionally, it does not provide any information about the mean or standard deviation of the data.