Mean Absolute Deviation (MAD) Statistics Example 3

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Example 3

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

Solution

  1. 1
    Step 1: Mean = 12+15+14+18+13+166=886≈14.67\frac{12+15+14+18+13+16}{6} = \frac{88}{6} \approx 14.67 cm.
  2. 2
    Step 2: Absolute deviations: ∣12−14.67∣=2.67|12-14.67|=2.67, ∣15−14.67∣=0.33|15-14.67|=0.33, ∣14−14.67∣=0.67|14-14.67|=0.67, ∣18−14.67∣=3.33|18-14.67|=3.33, ∣13−14.67∣=1.67|13-14.67|=1.67, ∣16−14.67∣=1.33|16-14.67|=1.33. MAD=2.67+0.33+0.67+3.33+1.67+1.336=106≈1.67MAD = \frac{2.67+0.33+0.67+3.33+1.67+1.33}{6} = \frac{10}{6} \approx 1.67 cm.

Answer

MAD≈1.67MAD \approx 1.67 cm. On average, each plant's height differs from the mean by about 1.67 cm.
Interpreting MAD in context means relating it to the original units of measurement. Here, the plants' heights vary by about 1.67 cm from the average on average, indicating moderate consistency in growth.

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 4 hard

A teacher claims that adding the same constant to every value in a data set does not change the MAD.

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