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January 28, 2015

January 28, 2015

Posted by **ash** on Tuesday, August 28, 2012 at 11:51pm.

- ap stats -
**Walter**, Sunday, January 6, 2013 at 12:22pmMinimum stays the same.

Q1 might increase or stay the same.

Median might increase or stay the same.

Q3 might increase or stay the same.

Maximum will increase.

Mean will increase.

Standard deviation will increase.

Minimum and maximum should be obvious. Q1, median and Q3 are based on position in the distribution and will go up if the next data point (in ascending value order) is different AND the addition of a new maximum changes the position of the quartile boundaries in the distribution.

Here is an interesting bonus problem to get more understanding of this: Suppose you have a distribution with n values and no two of them are equal, by adding 1 data point that is higher than the maximum Q1, the median, and Q3 change. What is the lowest possible value for n?

The Mean must go up any time you add a value greater that the mean the mean increases and a number greater than the maximum is certainly greater than the mean.

The standard deviation will increase because a number greater than the maximum will deviate from the mean more than the maximum and increase the overall spread.

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