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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.
Between Mean Median and Mode which are affected most by an outlier?
The mean is affected the most by an outlier.
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 measure is most affected by an outlier?
mean
Is the mean affected by a low outlier?
Yes.Yes.Yes.Yes.
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 would happen if a outlier was removed from the mean?
The answer depends on the nature of the outlier. Removing a very small outlier will increase the mean while removing a large outlier will reduce the mean.
Would a mean be smaller or larger if you leave out an outlier?
Depends on whether the outlier was too small or too large. If the outlier was too small, the mean without the outlier would be larger. Conversely, if the outlier was too large, the mean without the outlier would be smaller.
How do you determine how the outlier affects the mean median mode and range?
Calculate the mean, median, and range with the outlier, and then again without the outlier. Then find the difference. Mode will be unaffected by an outlier.
How does an outlier in a group of numbers affect the mean of the numbers?
The outlier skews the mean towards it.
If an outlier is included with a sample of 50 values all of which are the same what is the effect of the outlier on the mean?
By definition, an outlier will not have the same value as other data points in the dataset. So, the correct question is "What is the effect of an outlier on a dataset's mean." The answer is that the outlier moves the mean away from the value of the other 49 identical values. If the outlier is the "high tail" the mean is moved to a higher value. If the outlier is a "low tail" the mean is moved to a lower value.
