Mean Deviation: Mean deviation, also known as average deviation, is a measure of dispersion that quantifies the average difference between each data point in a dataset and the mean of that dataset. It provides information about how spread out the data is from the mean.
To calculate the mean deviation, follow these steps:
- Calculate the mean (average) of the dataset.
- Find the absolute difference between each data point and the mean.
- Sum up all the absolute differences.
- Divide the sum by the total number of data points.
The formula for mean deviation is:
Mean Deviation = (Sum of absolute differences) / (Total number of data points)
Mean deviation is less commonly used than other measures of dispersion like standard deviation and variance because it does not account for the direction of deviations from the mean.
Standard Deviation: Standard deviation is a widely used measure of dispersion that quantifies the average amount of deviation of data points from the mean. It provides a measure of how spread out the data is and how much individual data points vary from the average.
To calculate the standard deviation, follow these steps:
- Calculate the mean (average) of the dataset.
- Find the difference between each data point and the mean.
- Square each difference.
- Sum up all the squared differences.
- Divide the sum by the total number of data points.
- Take the square root of the result.
The formula for standard deviation is:
Standard Deviation = sqrt[(Sum of squared differences) / (Total number of data points)]
Standard deviation is a versatile measure that is widely used in statistical analysis and decision-making. It considers both the magnitude and direction of deviations from the mean.
Variance: Variance is another measure of dispersion that quantifies the average squared deviation of data points from the mean. It provides a measure of how much the individual data points differ from the average.
To calculate the variance, follow these steps:
- Calculate the mean (average) of the dataset.
- Find the difference between each data point and the mean.
- Square each difference.
- Sum up all the squared differences.
- Divide the sum by the total number of data points.
The formula for variance is:
Variance = (Sum of squared differences) / (Total number of data points)
Variance is commonly used in statistical analysis, but its value is in squared units, which can be difficult to interpret. The standard deviation, which is the square root of the variance, is often preferred as it is in the same unit as the original data and provides a more intuitive measure of dispersion.