# ap stats

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all students in a pe class completed a basketball free throw shooting event and the highest number of shots made was 32. the next day a student who had transferred into the school completed the event, making 35 shots. indicate whether adding the new student's score to the rest of the data made each of these summary statistics increase, decrease, or stay the same?

• ap stats -

Minimum 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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