SXXf2

In Equation 2, each measurement, X, is substrated from the mean, X, in order to find the difference between the measurement and the mean. Because some of the differences will be negative, the differences are squared to remove the negative sign. Each of the three squared differences is added and then the sum is divided by n-1, or the number of measurements minus 1, to find the average squared difference between the individual measurements and the mean. The rationale behind the use of n-1 instead of n to find the variance is discussed in Chapter 11.

Remember that the variance is the average of the squared differences between the individual values and the mean. The square root of the variance is called the standard deviation, written as s in statistical formulas and often abbreviated as SD in medical literature. It should be apparent now why the variance is abbreviated as s2. Both the standard deviation and the variance are measures of variability in a set of data.

To calculate the variance for Mrs. B., the following calculations are made. First, the difference between each of the three measurements and the mean is calculated as shown in Equations 3 through 5:

Then, each of the three differences is squared as shown in Equations 6 through 8:

(0.001)2 = 0.000001 (8) The three squared differences from equations 6 though 8 are then added.

Finally, this sum is divided by the number of measurements minus 1 as shown in equation 10. This number is the variance.

The square root of the variance is the SD. Therefore, s = SD = V0.000091 = 0.010 (11)

The mean or average BMD based on the three spine bone density measurements on Mrs. B. is 1.021 g/cm2. The variance and SD from this set of data on Mrs. B. are 0.000091 g/cm2 and 0.010 g/cm2 (with rounding), respectively. Because the SD represents a measure of variability of the individual measurements about the mean, it is now reasonable to ask, what proportion or percentage the SD is of the mean? This brings us to a discussion of the coefficient of variation.

Essentials of Human Physiology

Essentials of Human Physiology

This ebook provides an introductory explanation of the workings of the human body, with an effort to draw connections between the body systems and explain their interdependencies. A framework for the book is homeostasis and how the body maintains balance within each system. This is intended as a first introduction to physiology for a college-level course.

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