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Inferences from Sample Data

As stated before, many of the measurements you make will be approximately normally distributed. If you plot your data, and they fall roughly in the bell curve shape, then you can make the assumption that your underlying population distribution is normal.

Using this assumption, you can make several inferences about your population based on the sample data. First, approximate the population mean µ with the sample mean, , and the population standard deviation σ with the sample standard deviation, s. Then you can say that 68% of all data from the population will be within 1s of , 95% within 2s, and 99% within 3s. An example will illustrate.

Suppose you have urea nitrogen data with a sample mean of 15 mg/dL, and a sample standard deviation of 5 mg/dL. Then the following is true:

  • approximately 68% of healthy people will have urea nitrogen in the range ± 1s = 15 ± 5 mg/dL = 10-20 mg/dL.
  • approximately 95% of healthy people will have urea nitrogen in the range ± 2s = 15 ± 10 mg/dL = 5-25 mg/dL.
  • approximately 99% of healthy people will have urea nitrogen in the range ± 3s = 15 ± 15 mg/dL = 0-30 mg/dL.
These data can be used to set standards for healthy urea nitrogen levels. Most labs set the 95% window as reference ranges for all tests performed