How does removing the outlier from the data affect the mean and the median?

Answer 1

Examples are a good way to figure out statistical questions.

Say you have five people that are 61, 62, 63, 64, 65, and 90 inches tall. Obviously 90 is the outlier. With it in there, the mean is 67.5, and the median is 63.5 (halfway between 63 and 64). If you take the 90 out, the new average is 63, and the median is also 63. So basically, it affects mean more because when dealing with median it doesn't matter what the actual value of the outlier is. Whether it was 66 or 130, taking it out would do the same thing to the median. The mean depends on what the outlier IS.

Answer 2

Removing an outlier would affect the mean more than the median.
Since it's only one data value, removing it would only move the median over one spot in the list of values.
On the other hand, since the mean is the sum divided by the number of values, the ratio could be very different if the value of the outlier is different than the rest of the values. The mean would get more accurate without the outlier value, which is why they're sometimes removed.

For example, say you had 10 numbers

1
5
4
6
3
21
1
2
2
4

The median of these numbers is 3.5 (halfway between 3 and 4)

The mean of these numbers, however, is 4.6, which is greater than the median (because of the huge outlier).

Since 21 is obviously an outlier, let's remove it.

The median moves from 3.5 to 3.

The mean moves from 4.6 to 2.78, which is a big decrease.

Answer 3

Removing Outliers

Answer 4

If m is the mean of n observations and the outlier is x,
m2 = (nm - x) / (n - 1) =
(nm - m + m - x) / (n - 1) = m + (m - x) / (n - 1)

The median will shift at most 1/2 the interval between the middle two values. For large n, the median may not shift at all.

Answer 5

We remove an outlier because we can simply assume that there was some type of extreme experimental error, or something went wrong. The mean shouldn't be effected that much, but the median will be greatly effected.

Answer 6

An outlier is a data point that does not correspond with all the other data points. It will make the mean more accurate. If the outlier is higher, it will lower the mean. If the outlier is lower, it will raise the mean. When eliminated.

Answer 7

since outliers are data that really fall outside the norm, removing them makes sure the mean or median answers are not based off odd data.
for example, if a ten people read 20 pages an hour of some text book and one reads 200 pages per hour, the average pages/hour will be thrown off by the one person that seems to have way above average skills

Answer 8

Hi. Both should be minimally affected by removing outliers. But the median will be more effected. (The median only considers the extreme data points.)

Answer 9

Removing the outlier should make the data more accurate.