answersLogoWhite

0

The mean is one of those statistics that is more sensitive to outliers, and hence to mistakes in data, than it is to uncontaminated data.

Here's a pseudorandom sample of normally distributed values with mean 10 and variance 1 in sorted order:

8.3, 8.3, 9.0, 9.1, 9.2, 9.3, 9.5, 9.5, 9.7, 9.8, 9.9, 9.9, 10.2, 10.3, 10.4, 10.7, 10.9, 11.1, 11.3, 11.8

(Actually I've rounded them to the nearest 10th for easier reading.)

Their mean is 9.91.

Now let me add one outlier to the sample, say 4.2. Now the mean is 9.64. The original mean was only 0.09 away from the true mean, this one is four times as far away.

Of course it must also be said that one must be extremely careful about discarding data. Sometimes what appears to be an outlier has the most interesting information.

User Avatar

Wiki User

11y ago

Still curious? Ask our experts.

Chat with our AI personalities

EzraEzra
Faith is not about having all the answers, but learning to ask the right questions.
Chat with Ezra
RafaRafa
There's no fun in playing it safe. Why not try something a little unhinged?
Chat with Rafa
BlakeBlake
As your older brother, I've been where you are—maybe not exactly, but close enough.
Chat with Blake

Add your answer:

Earn +20 pts
Q: How the mean is affected by an outlier?
Write your answer...
Submit
Still have questions?
magnify glass
imp