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