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Interquartile Range Formula:
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The Interquartile Range (IQR) is a measure of statistical dispersion that represents the range between the first quartile (Q1) and the third quartile (Q3) of a dataset. It describes the spread of the middle 50% of the data values.
The calculator uses the IQR formula:
Where:
Explanation: The IQR measures the spread of the middle 50% of data points, making it a robust measure of variability that is less affected by outliers than the range.
Details: IQR is crucial for identifying outliers, understanding data distribution, and comparing variability between different datasets. It's commonly used in box plots and descriptive statistics.
Tips: Enter Q3 and Q1 values in the same units. Ensure Q3 is greater than Q1. The calculator will compute the IQR as the difference between these two quartiles.
Q1: What does IQR tell us about a dataset?
A: IQR indicates the spread of the middle 50% of data values. A larger IQR suggests greater variability in the central portion of the dataset.
Q2: How is IQR used to identify outliers?
A: Outliers are typically defined as values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR. This method is known as the Tukey fences method.
Q3: What's the difference between range and IQR?
A: Range considers all data points (max-min), while IQR focuses only on the middle 50%, making it more resistant to extreme values.
Q4: When should I use IQR instead of standard deviation?
A: Use IQR when your data has outliers or is skewed, as it's more robust. Use standard deviation for normally distributed data without outliers.
Q5: How do I calculate quartiles from raw data?
A: Sort the data, then Q1 is the median of the lower half, Q3 is the median of the upper half. Different methods exist for datasets with even/odd numbers of observations.