a business statics student has determined 9 out of the 10 deviations from the me

Question

a business statics student has determined 9 out of the 10 deviations from the mean for a data set. the first nine deviations has a sum of -2 and the mean of the data set is 20 A business statistics student has determined 9 of the 10 deviations from the mean for a data set. The first nine deviations has a sum of -2 and the mean of the data set is 20. Which of the following will be the correct observation by the student? O The last data element has no freedom to vary, because the last deviation must be 2 The last data element can be any value at all because there are not sufficient restrictions place on it. O The last data element must be less than the mean. O The last data element must be exactly 23 Submit

Explanation / Answer

We know that the sum of all deviations from mean is 0.

Let the 10th deviation be x.

Then, sum of all deviations = 0

=> Sum of first 9 deviations + x = 0

=> -2 + x = 0

=> x = 2

So, the first option is correct.

The last data element has no freedom to vary, because the last deviation must be 2.

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