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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.
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How are the mean and standard deviation affected by an outlier?
The mean is "pushed" in the direction of the outlier. The standard deviation increases.
Which of the following is least affected if an extreme high outlier is added to your data mean median or standard deviation or ALL?
The median is least affected by an extreme outlier. Mean and standard deviation ARE affected by extreme outliers.
How does the outlier affect the mean of the data?
An outlier does affect the mean of the data. How it's affected depends on how many data points there are, how far from the data the outlier is, whether it is greater than the mean (increases mean) or less than the mean (decreases the mean).
How would the outlier affect the mean and median of the data?
An outlier will pull the mean and median towards itself. The extent to which the mean is affected will depend on the number of observations as well as the magnitude of the outlier. The median will change by a half-step.
What is the value of a data set most likely to be affected by an outlier?
The range.
