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EXERCISE

MEAN, STANDARD DEVIATION,
AND 95% AND 99% OF THE
NORMAL CURVE

STATISTICAL TECHNIQUE IN REVIEW
Mean (X) is a measure of central tendency and is the sum of the raw scores divided by the number of scores being summed. Standard deviation (SD) is calculated to measure dispersion or the spread of scores from the mean (Burns & Grove, 2007). The larger the value of the standard deviation for study variables, the greater the dispersion or variability of the scores for the variable in a distribution. (See Exercise 16 for a detailed discussion of mean and standard deviation.)
Since the theoretical normal curve is symmetrical and unimodal, the mean, median, and mode are equal in the normal curve (see Figure 18-1). In the normal …show more content…

In this example, 490 + 1.96 (100) = 686, and 490 - 1.96 (100) = 294. Thus 95% of scores lie between 294 and 686, expressed as (294, 686). Since 95% of the scores are between 294 and
686, this leaves 5% of the scores outside this interval. Since a normal curve is symmetric, one-half of the scores, or 2.5%, are at each end of this distribution.
To find where 99% of scores lie,Z ± 2.58 (SD), where 490 + 2.58 (100) = 748 and 490 - 2.58 (100) = 232.
Thus, 99% of the SAT scores lie between 232 and 748, which is expressed as (232, 748). Since the distribution of these scores is normal, 99% of the scores are between 232 and 748 and 0.5% of the scores are at each end of this distribution.
FIGURE 18-2 'ft Distribution of SAT Scores

SD=100

x = 490
Mean

RESEARCH ARTICLE
Source: Corless, I. B., Nicholas, P. K., McGibbon, C. A., & Wilson, C, (2004). Weight change, body image, and quality of life in HIV disease: A pilot study. Applied Nursing Research 77(4), 292-6.

Introduction
The purpose of this pilot study [conducted by Corless and colleagues (2004)] was to investigate the relationships of weight change, body image, length of time with HIV/AIDS diagnosis, and quality of life in individuals with HIV disease (Corless et al., 2004, p. 292). The sample consisted of 40 subjects: 23 men and 17 women. The HIV-positive adults in a primary care clinic were asked to participate, so this study has a sample of

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