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IB Mathematics SL Prep

Category - IB Mathematics

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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 standard deviation of these groundwater elevation readings?
  1. 3.01
  2. 8.76
  3. 9.08
  4. None of the above.
Explanation
Answer: A - The standard deviation of the groundwater elevation readings is 3.01.

Solution

Use the standard deviation (s) equation

s = square root [ ?(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

s = 3.01
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