Interquartile range
The interquartile range (IQR) is a measure of statistical dispersion that describes the spread of the middle 50% of a data set. It is calculated by finding the difference between the first quartile (Q1), which marks the 25th percentile, and the third quartile (Q3), which marks the 75th percentile. The formula is:
The IQR is useful for identifying outliers and understanding the variability of the data, as it focuses on the central portion while minimizing the influence of extreme values. A larger IQR indicates greater variability among the middle half of the data, while a smaller IQR suggests that the values are more closely clustered around the median.
Part 1: Interquartile range (IQR)
Key Points for Studying Interquartile Range (IQR)
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Definition: The IQR is a measure of statistical dispersion that represents the range between the first quartile (Q1) and the third quartile (Q3) of a data set.
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Quartiles:
- Q1 (First Quartile): The median of the lower half of the data set; 25% of the data points fall below this value.
- Q3 (Third Quartile): The median of the upper half of the data set; 75% of the data points fall below this value.
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Formula:
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Purpose: The IQR is used to measure the spread of the middle 50% of a data set, providing insights into its variability.
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Outlier Detection: The IQR is useful for identifying outliers. Typically, any data point below or above is considered an outlier.
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Resilience: The IQR is less affected by extreme values (outliers) than the overall range, making it a more robust measure of variability.
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Visualization: IQR is often represented in box plots, highlighting the central 50% of the data.
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Application: Commonly used in descriptive statistics, data analysis, and box plot construction across various fields including finance, research, and quality control.
By mastering these points about IQR, one can effectively analyze and interpret data variability in various contexts.