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Chapter 1: Q. 97 (page 72)

Phosphate levels The level of various substances in the blood influences our health. Here are measurements of the level of phosphate in the blood of a patient, in milligrams of phosphate per deciliter of blood, made on 6 consecutive visits to a clinic: 5.6, 5.2, 4.6, 4.9, 5.7, 6.4. A graph of only 6 observations gives little information, so we proceed to compute the mean and standard deviation. (a) Find the standard deviation from its definition. That is, find the deviations of each observation from the mean, square the deviations, then obtain the variance and the standard deviation. (b) Interpret the value of sx you obtained in (a)

Short Answer

Expert verified

a. x炉=5.4mg/dI and sx=0.6419mg/dI

b. The phosphate level varies at 0.6418 mg/dI

Step by step solution

01

Finding the value of the standard deviation  

a. the mean value of all question data is 5.6+5.2+4.6+4.95.7+6.46=5.4mg/dI

Assume xiis the data value then deviation is Xi-X. so the square deviation is

Now, the variance is the sum of the total values divided by (n-1).

sx2=0.04+0.04+0.06+0.25+0.09+16-1=0.419

So the standard deviation is 0.419=0.6419mg/dI

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