What is the First Step When Calculating the Mean Absolute Deviation?

The first step when calculating the mean absolute deviation (MAD) is to calculate the mean (average) of the data set.

To effectively determine the mean absolute deviation, it's essential to follow these steps:

1. Calculate the Mean: Find the average of all the numbers in the data set. This is done by adding all the values together and dividing by the total number of values.

2. Calculate the Absolute Deviations: Determine how far each individual data point is from the mean. Since we are interested in the distance from the mean, we use absolute values. This means we ignore whether the difference is positive or negative; we only care about the magnitude.

3. Calculate the Mean of the Absolute Deviations: Find the average of all the absolute deviations calculated in the previous step. This average distance is the Mean Absolute Deviation.

Example:

Let's say you have the following data set: 2, 4, 6, 8, 10

1. Calculate the Mean: (2 + 4 + 6 + 8 + 10) / 5 = 6

2. Calculate the Absolute Deviations:

   • |2 - 6| = 4
   • |4 - 6| = 2
   • |6 - 6| = 0
   • |8 - 6| = 2
   • |10 - 6| = 4

3. Calculate the Mean of the Absolute Deviations: (4 + 2 + 0 + 2 + 4) / 5 = 2.4

Therefore, the mean absolute deviation for this data set is 2.4.