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  1. Without calculating, compare the means and
    the MADs of the two dato sets.
  2. The means are ?
    The MADs are the same
    different

Ask by Ryan Horton. in the United States
Mar 25,2025

Solución de inteligencia artificial de Upstudy

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The means are different, and the MADs are the same.

Solución

Let’s suppose we have two data sets that contain the same “shape” of values, but one set is obtained by adding a constant to every number in the other. In that case:
  • The mean of a data set is sensitive to adding a constant. If a constant is added to every value, the mean increases by .
  • In contrast, the mean absolute deviation (MAD), which measures the average distance from the mean, is unaffected by such a translation; the distances from the mean remain the same.
Without doing any calculations, if the only difference between the two data sets is a constant shift, then:
  • The means of the two data sets are different (by exactly the constant that was added).
  • The MADs are the same.
Thus, without crunching numbers, we can state that the means are different and the MADs are the same.

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The Deep Dive

When comparing the means of two data sets without calculating them, you can analyze the distributions visually or based on their descriptions. If one data set has values that are consistently lower or higher than the other, it’s likely that its mean will reflect that trend.
As for the Mean Absolute Deviation (MAD), if both data sets show similar variation around their respective means, it’s possible for their MADs to be the same. However, if one data set is more spread out than the other, their MADs will differ. So, always consider the distribution and spread when making these comparisons!

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