Mean Absolute Deviation (MAD) Statistics Example 4

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

Example 4

hard
A teacher claims that adding the same constant to every value in a data set does not change the MAD. Test this claim with the data set {5, 10, 15, 20, 25} by adding 100 to each value and comparing the MADs.

Solution

  1. 1
    Step 1: Original: mean = 15, deviations = {10,5,0,5,10}, MAD = 305=6\frac{30}{5} = 6. New data: {105,110,115,120,125}, mean = 115, deviations = {10,5,0,5,10}, MAD = 305=6\frac{30}{5} = 6.
  2. 2
    Step 2: Both MADs equal 6. Adding a constant shifts all values and the mean by the same amount, so deviations from the mean remain unchanged. The teacher's claim is correct.

Answer

Both MADs equal 6. Adding a constant to every value does not change the MAD because the mean shifts by the same constant, preserving all deviations.
MAD measures spread, which is a property of the relative distances between data points and their mean. Shifting all data by a constant translates the entire distribution without changing its shape or spread. This is a general property of all deviation-based measures of spread.

About Mean Absolute Deviation (MAD)

The Mean Absolute Deviation (MAD) is the average of the absolute distances between each data point and the mean of the dataset. It measures how spread out data values are from the center, with larger MAD values indicating more variability.

Learn more about Mean Absolute Deviation (MAD) →

More Mean Absolute Deviation (MAD) Examples

Example 1 easy

Find the mean absolute deviation (MAD) of the data set: 4, 6, 8, 10, 12.

Example 2 medium

Two data sets: A = {10, 10, 10, 10, 10} and B = {2, 6, 10, 14, 18}. Both have a mean of 10. Calculat

Example 3 medium

The heights (in cm) of 6 plants are: 12, 15, 14, 18, 13, 16. Calculate the MAD and interpret the res

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