Understanding Statistical Averages
The term "average" commonly refers to the arithmetic mean, but there are several types of averages used in statistics. The mean is the sum of all values divided by the count. The median is the middle value when data is sorted. The mode is the most frequently occurring value. Each provides different insights into your data.
When to Use Each Average
Use the mean for normally distributed data without extreme outliers. Use the median when data is skewed or has outliers (like income data). Use the mode for categorical data or to find the most common value. The geometric mean is useful for growth rates and ratios, while the harmonic mean is best for rates and speeds.
Standard Deviation
Standard deviation measures how spread out the values are from the mean. A low standard deviation means values are clustered close to the mean, while a high standard deviation indicates the values are spread over a wider range. It is one of the most important measures of variability in statistics.