How to run

Topics: Standard deviation, Normal distribution, Arithmetic mean Pages: 5 (1293 words) Published: May 3, 2014
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 curve, 95% of the scores will be within 1.96 standard deviations of the mean, and 99% of scores are within 2.58 standard deviations of the mean. Figure 18-1 demonstrates the normal curve, with a.X = 0. The formula used to calculate the 95% rule to determine where 95% of the scores for the normal curve lie is: X±1.96(SD)

The formula used to calculate the 99% rule to determine where 99% of the scores for the normal curve lie is:
X ± 2.58 (SD)
FIGURE 18-1 • The Normal Curve
Mean
Median
Mode

Standard deviation -3
Zscore
-2.58

-+2.58

131

133

Mean, Standard Deviation, and 95% and 99% of the Normal Curve • EXERCISE 18

Participants reported a net increase in weight from 3 months prior (M= 2.4 Ib, SD - 12.9 Ib) and 12 months prior (M = 10.9 Ib, SD = 19.1 Ib) and that their weight was greater than their ideal weight (M = 9.2 Ib, SD = 22.9 Ib). SDs for the data indicated a wide range on weight at both 3 and 12 months before participation in the study.

Body image scores (0-100 scale) were significantly (F(1 37) = 5.41, p =.03) higher for women (73.1 ± 17.0) than men (60.2 ± 17.0). Although HIV-positive participants had slightly higher body image scores (M = 68.0, SD = 17.0) compared with participants with AIDS (M = 60.5, SD = 18.8), there was no significant difference (F(1 ,7, = 1.56, p —.22) in body image scores between [those with HIV and AIDS]. There was a weak, but significant, inverse association between body image score and weight changes from 3 months prior (r = -.30, p =.04). Body image and weight scores are summarized in Table 1" (Corless et al, 2004, p. 294).

TABLE 1 •

Body Image and Weight Measures for Men and Women
GENDER
Male

Female

Mean

Body image
Weight change last 12 months
Weight change last 3 months
Weight relative to ideal
Body weight ratio

SD

Mean

SD

60.22
10.26

16.98
22.40
15.87
22,93
33.97

73.07
11.94
1.47

13.63

14.44
67.56

22.57
34.44

3.05
5.48
53.66

16.93
7.32

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), p. 294.

"A summary of quality-of-life scores for men and women is shown in Table 2. The scales of the MOS-HIV Quality of Life instrument include General Health Perceptions, Physical Functioning, Role Functioning, Social Functioning, Cognitive Functioning, Pain, Mental Health, Vitality, Health Distress, Quality of Life, and Heath Transition. There were no significant differences between quality of life scores between men and women. Men did have lower scores on some MOS-HIV scales (Cognitive Functioning, Pain, Quality of Life, and Health Transition) and women were lower on others (Vitality and Health Distress). In addition, there were a number of differences in the relationships between quality of life scores, body image, and body weight.... The positive correlations indicated that improved quality of life was associated with improved body image" (Corless et al., 2004, pp. 294-5).

132

EXERCISE 18

Mean, Standard Deviation, and 95% and 99% of the Normal Curve MMMMMM^^

The data described below are the verbal SAT scores for high school...
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