For this assignment you will compare the dot plots provided to answer questions.

Question

For this assignment you will compare the dot plots provided to answer questions. The blue dots represent sample data values. When two data values are the same, they stack one on top of the other to show frequency as a height. The sample mean (x bar) and sample standard deviation (s) are given for all dot plots on this worksheet. Compare the following two dot plots x bar = 2.5 and s = 2.09 x bar = 2.7 and s = 2.23 a. What happens to the sample mean when a point was moved to the right? b. What happens to the sample standard deviation when a point was moved to the right?

Explanation / Answer

(a)
When a point is moved to the right i.e. a point from 2 is added to 6. This will cause the change in the mean of the sample.
Effective 4 will be added to the sum of all and when we divide it by 20, will give the change in the mean of the sample.
4/20 = 0.2
Similar change we see in the two plots where mean is changed fomr 2.5 to 2.7 i.e. 0.2 change in the mean.

(b)
In case of standard deviation, it changes from 2.09 to 2.23. i.e. the change of 2.23 - 2.09 = 0.14.

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