Mean Absolute Deviation Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Calculate the Mean Absolute Deviation (MAD) for {2,5,7,10,6}\{2, 5, 7, 10, 6\} and explain what it measures.

Solution

  1. 1
    Mean: xห‰=(2+5+7+10+6)/5=30/5=6\bar{x} = (2+5+7+10+6)/5 = 30/5 = 6
  2. 2
    Absolute deviations: โˆฃ2โˆ’6โˆฃ=4|2-6|=4, โˆฃ5โˆ’6โˆฃ=1|5-6|=1, โˆฃ7โˆ’6โˆฃ=1|7-6|=1, โˆฃ10โˆ’6โˆฃ=4|10-6|=4, โˆฃ6โˆ’6โˆฃ=0|6-6|=0
  3. 3
    MAD=4+1+1+4+05=105=2MAD = \frac{4+1+1+4+0}{5} = \frac{10}{5} = 2
  4. 4
    Interpretation: on average, each value is 2 units away from the mean

Answer

MAD=2MAD = 2. On average, each data point deviates from the mean by 2 units.
MAD measures the average absolute distance of data points from the mean. Unlike variance (which squares deviations), MAD keeps deviations in the original units. It is more interpretable than variance and more resistant to extreme values than variance.

About Mean Absolute Deviation

The average distance between each data value and the mean of the data set. Calculated by finding the mean, computing the absolute value of each deviation from the mean, and averaging those absolute deviations.

Learn more about Mean Absolute Deviation โ†’

More Mean Absolute Deviation Examples

Example 2 medium

Compare MAD and standard deviation for the data [formula]. Calculate both and explain when MAD is pr

Example 3 easy

Calculate MAD for daily temperatures (ยฐF): [formula].

Example 4 hard

Data set A: [formula] and Data set B: [formula]. Both have mean 5. Calculate MAD for each and explai

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