- 1). Find the difference between the number of standard deviations away from the mean for the lowest quartile and 0.5. Use 0.6745 as an approximation. For example, 0.6745 minus 0.5 equals 0.1745.
- 2). Divide the difference by 0.5 and multiply by 100 to determine the lowest quartile's percentage within the half standard deviation range. For example, 0.1745 divided by 0.5 equals 0.349, which multiplied by 100 equals 34.9 percent.
- 3). Determine the portion of the distribution within the range of half a standard deviation that is below the lowest quartile. Multiply the lowest quartile's percentage from above by the distribution within the range. For example, 15 percent of a normal distribution falls between one-half and one standard deviation from the mean. Fifteen percent multiplied by 0.349 equals 5.235 percent.
- 4). Add the result to 19.1 percent, the percent of a normal distribution that falls between the mean and 0.5 standard deviations. Subtract the sum from 50 percent, the percent of a normal distribution that falls below the median. For example, 50 minus 24.335 equals 25.665 percent.
- 5). Record the result as the probability that a value in a normal distribution of percentages will fall within the lowest quartile.
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