Deviation is a fundamental concept that describes how something differs from a standard or expected value. In everyday language, it means departing from an established course or norm. In statistics, deviation specifically refers to the difference between an observed data point and the mean value of a dataset. Here we can see data points and their deviations from the mean line.
There are several types of deviation in statistics. Absolute deviation is the absolute difference between a value and the mean. Standard deviation measures how spread out the data points are from the mean. Mean absolute deviation is the average of all absolute deviations. Each type provides different insights into data variability.
The standard deviation formula calculates how spread out data points are from the mean. We square each deviation to eliminate negative values, sum them up, divide by the number of values, and take the square root. This table shows the calculation step by step for our data set, resulting in a standard deviation of 1.25.
The normal distribution shows how deviation relates to probability. In a bell-shaped normal curve, about 68 percent of data falls within one standard deviation of the mean, 95 percent within two standard deviations, and 99.7 percent within three standard deviations. This relationship helps us understand how unusual or typical a particular deviation is.
Deviation has many practical applications across different fields. In quality control, manufacturers use deviation to set tolerances and ensure products meet standards. In finance, standard deviation measures investment risk and volatility. Researchers use deviation to analyze data reliability. In medicine, deviation helps identify normal versus abnormal test results. In education, deviation analysis helps create fair grading curves. Understanding deviation is essential for making informed decisions in data-driven environments.