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Coefficient of Dispersion Formula:
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The Coefficient of Dispersion (COD) is a statistical measure that quantifies the relative variability or dispersion of a dataset. It is calculated as the ratio of the difference between the third and first quartiles to their sum.
The calculator uses the COD formula:
Where:
Explanation: The formula measures the spread of the middle 50% of data relative to the center of that range. A higher COD indicates greater variability in the dataset.
Details: COD is particularly useful in economics, real estate assessment, and quality control to measure relative variability without being influenced by extreme outliers. It helps compare dispersion across different datasets with different scales.
Tips: Enter the first quartile (Q1) and third quartile (Q3) values. Both values must be positive numbers, and Q3 must be greater than Q1 for a valid calculation.
Q1: What does a COD value of 0 indicate?
A: A COD value of 0 indicates no variability in the middle 50% of the data, meaning Q1 and Q3 are equal.
Q2: What is the range of possible COD values?
A: COD values range between 0 and 1. A value closer to 0 indicates less variability, while a value closer to 1 indicates greater variability.
Q3: How is COD different from other measures of dispersion?
A: Unlike standard deviation or variance, COD is a relative measure that isn't affected by the units of measurement, making it useful for comparing variability across different datasets.
Q4: When should I use COD instead of other dispersion measures?
A: COD is particularly useful when you want to compare variability between datasets with different means or when working with data that might have outliers affecting other measures.
Q5: Can COD be negative?
A: No, since Q3 is always greater than or equal to Q1, the numerator (Q3 - Q1) is always non-negative, and the denominator (Q3 + Q1) is always positive, resulting in a non-negative COD value.