Question

explaining mean absolute deviation calc
explain the steps in calculating the mean absolute
deviation of a set of data.

Explanation:

Step1: Calculate the mean

First, find the mean (\(\bar{x}\)) of the data set. The mean is calculated by summing all the data points (\(x_i\)) and dividing by the number of data points (\(n\)). The formula for the mean is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}\).

Step2: Find the absolute deviations

For each data point \(x_i\), find the absolute deviation from the mean, which is \(|x_i-\bar{x}|\). This gives the distance of each data point from the mean, ignoring the direction (positive or negative).

Step3: Calculate the mean of absolute deviations

Sum up all the absolute deviations from Step 2, and then divide this sum by the number of data points \(n\). The formula for the mean absolute deviation (MAD) is \(MAD=\frac{\sum_{i = 1}^{n}|x_i - \bar{x}|}{n}\).

Answer:

1. Calculate the mean (\(\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}\)) of the data set.
2. For each data point \(x_i\), find the absolute deviation \(|x_i-\bar{x}|\).
3. Sum all the absolute deviations and divide by the number of data points \(n\) (using \(MAD=\frac{\sum_{i = 1}^{n}|x_i - \bar{x}|}{n}\)) to get the mean absolute deviation.