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DSST Principles of Statistics Exam Prep

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The given numbers are daily groundwater elevation readings from a monitoring well taken during a month experiencing snowmelt and extended rainfall events.

7.6, 7.7, 4.3, 5.9, 5.0, 10.5, 7.7, 9.5, 12.0, 12.6, 6.5, 8.3, 8.2, 13.2, 12.6, 13.6, 14.1, 13.5, 11.5, 12.0, 10.4, 10.8, 13.1, 12.5, 10.4, 13.0, 14.1, 15.1

What is the sample variance of these groundwater elevation readings?

  1. 8.764
  2. 9.089
  3. 10.56
  4. None of the above
Explanation

Answer: B - The sample variance of the groundwater elevation readings is 9.089.

Use the sample variance (s2) equation

s2 = ?(sample value - sample mean)2/(number of samples-1)

Where Number of samples = 28

Sample mean = ?(sample values)/number of samples

= 295.7/28 = 10.56

?(sample value - sample mean)2 = (7.6-10.56)2+(7.7-10.56) 2 = 245.4

s2 = 245.4/27 = 9.089

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