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# Explain why the median might be considered a more reliable measure of central tendency than the mean for a data set that is thought to contain an outlier.

2 years ago

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H

Herbert Williamson

4 Answers

Brian H
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The mean is affected by data size - an outlier can skew the mean away from where the majority of the data lies.

The median is ** not dependent **on the size of data, it

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K

Kim Fung Lai

Lets consider a set of numbers, say,

1,1,2,2,3,3,4,4,5

In this case, the median is 3 while the mean is 2.77.

If one of the data is replaced by an extreme number, say 5 becomes 100, the set of number will become:

1,1,2,2,3,3,4,4,100

The median is still 3! However, the mean will become 13.3. That’s why we say that the mean is easily influenced a lot by outliers (extreme values in a set of numbers). And we would say the median is more reliable to measure the central tendency in such cases.

J

Jiayao Lin

Both can show the central tendency of a data set. However, in this case, an outlier can be either the lowest or the highest value in a dataset, which can significantly bias the mean value with the outlier included than excluded. While the median of a dataset is more fixed in this case and thus more reliable.

Heena T
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The mean is the most frequently used measure of central tendency because it uses all values in the data set to give you an average.

However, calculating the mean of a data set that contains an outlier (an extremely large or small number that is too far away from the rest of the data points) would produce a misleading answer.

For data with outliers, the median is better than the mean because extremely large values don’t influence it.

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