Learn why the median is the most accurate measure of central tendency for right-skewed data, avoiding distortion caused by outliers. Ideal for data analysis and Google Cloud certification.
Table of Contents
Question
You have a dataset of a classroom of students and their heights, and you are attempting to use the mean to find the measure of central tendency. However, your data is skewed towards the right. What should be your means of measuring central tendency?
A. The median
B. The standard deviation
C. The mode
D. The range
Answer
A. The median
Explanation
When a dataset is skewed to the right, the mean is disproportionately affected by extreme values (outliers) in the longer tail of the distribution. This makes the mean less representative of the central tendency.
The median, on the other hand, is the middle value in an ordered dataset and remains unaffected by outliers or skewness. It provides a more robust and accurate measure of central tendency in such cases.
For example, in a dataset of student heights where most values are clustered at lower ranges but a few extreme values (e.g., very tall students) pull the distribution to the right, the mean will be higher than most typical heights. The median, however, will reflect the “typical” height more accurately because it divides the dataset into two equal halves.
Other options:
B. The standard deviation: This measures variability, not central tendency.
C. The mode: While useful for categorical data or identifying the most frequent value, it is not ideal for skewed distributions.
D. The range: This measures dispersion (difference between maximum and minimum values) and does not represent central tendency.
Thus, for right-skewed data, always use the median as it best represents the central tendency without being influenced by extreme values.
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