3. If a data set consists of measurements from an experiment that is repeated, t

Question

3. If a data set consists of measurements from an experiment that is repeated, then is the data good or bad if the standard deviation of the measurements is high? Explain your answer.

(4) (a) If the mean of a data set is 10, and the z-score of the data value 5 (in the data set) is -2, find the standard deviation of the data set.
(b) If the standard deviation of a particular data set is 4, the mean of the data set is 12, and the z-score of a particular data value, in the data set, is 30, find the numerical value of the data value.

Explanation / Answer

Answer to the questions is as follows:

3. The data is bad, because if the data points are repeated then the standard deviation should drop.
It is infact high, and hence data is bad

4a.

Mean = 10, Z = -2 for X=5

We know that: (X-Mean) / Sigma = Z

Using this: 5-10/Sigma = -2
Sigma = 2.5

b. Sigma = 4
Mean =12
Z = 30
X = ?
X-Mean/Sigma = Z
X = Z*Sigma+Mean = 30*4+12 =132

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