Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321755936
ISBN 13: 978-0-32175-593-3

Chapter 2 - Methods for Describing Sets of Data - Exercises 2.48 - 2.70 - Applying the Concepts - Intermediate - Page 59: 2.68b

Answer

We recommend the median, as it is less affected by the extreme observations.

Work Step by Step

Observing the data items in the column "Ant Species", we see two unusually large observations ($52$ and $49$), while the other nine are single-digit values. These two extreme observations will "drag" the mean rightwards (in the positive direction), and the mean will not represent the dataset very well. The median, however is less affected by these extreme values, as they are positioned at the last two places in a ranked set. They may have as well been $10$ and $11$. Or $900$ and $1000$. In neither case would the middle position of the median be affected. Recall that the median (here: $5$) is such that $5$ observations are below or equal to it, and $5$ observations are above or equal to it. We recommend the median.
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