Hi! Your clicks on ads help us keep this blog going strong. If you like what you see, please consider clicking on any ads. Thanks for your support!
Dispersion refers to the extent to which a dataset is spread out, measuring the variability of data points.
High dispersion indicates wide-ranging data points, while low dispersion shows clustering around a central value.
Key measures of dispersion include:
Range: The difference between the maximum and minimum values. It provides a basic sense of spread but can be influenced by outliers.
Interquartile Range (IQR): The difference between the 75th percentile (Q3) and the 25th percentile (Q1), showing the spread of the middle 50% of the data. It is less sensitive to outliers.
Variance: The average of the squared differences from the mean, quantifying how far each data point is from the mean. Its squared units make it less directly interpretable.
Standard Deviation: The square root of the variance, bringing the units back to the original scale, making it easily interpretable.
Mean Absolute Deviation: The average of the absolute differences between each data point and the mean, giving a direct measure of spread.
Coefficient of Variation (CV): A standardized measure of dispersion, calculated as the ratio of the standard deviation to the mean, allowing for comparison between datasets with different units or scales.
Example:
A pharmaceutical company produces a batch of tablets, each intended to contain 100mg of an active pharmaceutical ingredient (API).
A sample shows API concentrations (in mg): 98, 102, 99, 101, 100, 98, 103, 97, 102, 100.
The dispersion can be analyzed by calculating the standard deviation:
Mean concentration is 100mg.
Differences from the mean: -2, 2, -1, 1, 0, -2, 3, -3, 2, 0.
Squared differences: 4, 4, 1, 1, 0, 4, 9, 9, 4, 0.
Variance: 3.6 mg^2.
Standard deviation: 3.6≈1.9𝑚𝑔3.6≈1.9mg.
This standard deviation indicates the variability in API concentrations, with a lower value suggesting more consistency, ensuring the efficacy and safety of the medication. This type of analysis is crucial for maintaining the quality of pharmaceutical products.
Hi! Your clicks on ads help us keep this blog going strong. If you like what you see, please consider clicking on any ads. Thanks for your support!