While normal distributions are all not the characteristic: a given standard deviation from the mean always"cuts off the sam proportion or percentage of scores in all normal distributions Specifically, one standard deviation above and below the mean includes about 68% of the scores; two(actually, about 1.96) standard deviations above and below the an include 95 percent, and three include more than 99.7 percent of the Major characteristics These percentages are worth committing to memory: 68-95-99.7 lower halves of the distribution of scores are mages of eat Second it is unimodal the mean. median and mode are all in the same place in the center of the distribution(at the top of the bell curve), the distribution is thus highest in the middle, and curves downward toward the top and bottom of the distribution and lower tails of the distribution never actually touch the baseline known as the x-axis3 5 6 Major characteristics • It is symmetrical, meaning that the upper and lower halves of the distribution of scores are mirror images of each other. • Second it is unimodal; the mean, median and mode are all in the same place, in the center of the distribution (at the top of the bell curve); the distribution is thus highest in the middle, and curves downward toward the top and bottom of the distribution. • Third it is asymptotic, meaning that the upper and lower tails of the distribution never actually touch the baseline, known as the X-axis. 4 7 • While normal distributions are all not the same, they share an important characteristic: a given standard deviation from the mean always “cuts off” the same proportion or percentage of scores in all normal distributions. • Specifically, one standard deviation above and below the mean includes about 68% of the scores; two (actually, about 1.96) standard deviations above and below the mean include 95 percent, and three include more than 99.7 percent of the scores. 8 These percentages are worth committing to memory: 68-95-99.7