5. Consider the following four samples. Table A.2 Sample Observations in the Sam

Question

5.     Consider the following four samples.

Table A.2

Sample

Observations in the Sample

Sample 1

1     1    1     1      1

Sample 2

0     0    5    10    10

Sample 3

1    1     1      1   50

Sample 4

1     1     5    10   10

a.    Which of the four samples would havethe smallest standard deviation? Provide reasoning (Note:Don’t need to calculate a standard deviation).

b.    Which of the four samples would havethe largest standard deviation? Provide reasoning. (Note:Don’t need to calculate a standard deviation).

Sample

Observations in the Sample

Sample 1

1     1    1     1      1

Sample 2

0     0    5    10    10

Sample 3

1    1     1      1   50

Sample 4

1     1     5    10   10

Explanation / Answer

Standard deviation is defined as the average differencebetween the observed values and the average. In other words, if thestandard deviation is huge, then the observed values deviate a lotfrom the mean. a) sample 1, because all the values are the same, there is novariation at all. In fact, standard deviation is 0 here. b) sample 3, because we have one value 50 that deviates a lotfrom the rest. This outlier causes the most variation than samples2 and 4

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