Calculate mean absolute deviation

Learning Objectives Define key statistical terms such as mean, deviation, and absolute value. Calculate the mean of a given data set. Determine the deviation of each data point from the mean. Explain the purpose of using absolute values in deviation calculations. Calculate the Mean Absolute Deviation (MAD) for a given set of data. Interpret what a higher or lower MAD indicates about a data set's variability. Apply the steps for calculating MAD to real-world data scenarios. Have you ever wondered how consistent a basketball player's scores are, or how spread out the temperatures are in your city? 🤔 We can use a special number to measure how 'spread out' data is! In this lesson, you'll learn how to calculate the Mean Absolute Deviation (MAD), a pow...

TermDefinitionExample Data SetA collection of numbers or values that represent information about something.The ages of students in a club: {12, 13, 12, 14, 13} Mean (Average)The sum of all the values in a data set divided by the number of values in the set. It's a measure of central tendency.For the data set {2, 4, 6}, the mean is (2+4+6)/3 = 12/3 = 4. DeviationThe difference between a single data point and the mean of the data set. It shows how far each point is from the average.If the mean is 5 and a data point is 7, the deviation is 7 - 5 = 2. If a data point is 3, the deviation is 3 - 5 = -2. Absolute ValueThe distance of a number from zero on a number line, always expressed as a positive value. It's denoted by vertical bars around the number (e.g., | -5 | = 5).The absolute...

Formula for Mean $\bar{x} = \frac{\sum x}{n}$ To find the mean ($\bar{x}$), sum all the data points ($\sum x$) and divide by the total number of data points ($n$). This is the first step in calculating MAD. Formula for Deviation Deviation $= x - \bar{x}$ For each data point ($x$), subtract the mean ($\bar{x}$) to find its deviation. This tells you how far and in what direction each point is from the average. Formula for Absolute Deviation Absolute Deviation $= |x - \bar{x}|$ Take the absolute value of each deviation. This ensures all differences are positive, as we are interested in the distance from the mean, not the direction. Formula for Mean Absolute Deviation (MAD) $MAD = \frac{\sum |x - \bar{x}|}{n}$ To find the MAD, sum all the absolute deviations ($\s...