I am not sure if this is correct, but here's my reasoning based on statistics: avg IQ is 100, and under a normalized bell curve that would include 95% of the population, so to move 3 std dev above or below would be:
1 std dev includes: 100-95 = 5. 5/2 = 2.5 so 2.5 + 95 => 97.5%
2 std dev includes: 100 - 97.5 = 2.5. 2.5/2 = 1.25 so 97.5 + 1.25 = 98.75
3 std dev includes: 100 - 98.75 = 1.25. 1.25/2 = .625 so 98.75 + .625 = 99.375
100 - 99.375 is percentage of population who are geniuses (more than 3 std dev above the mean) - about 0.6%, which is more than 1 in 200 people - That seems like a lot but unfortunately I'm not one of them :)
In a normal distribution, approximately 68% of the population falls within one standard deviation of the mean, and about 95% falls within two standard deviations. Therefore, to find the percentage of the population between one standard deviation below the mean and two standard deviations above the mean, you would calculate 95% (within two standard deviations) minus 34% (the portion below one standard deviation), resulting in approximately 61% of the population.
How many standard deviations is 16.50 from the mean?
You can't average means with standard deviations. What are you trying to do with the two sets of data?
The z-score of a value indicates how many standard deviations it is from the mean. If a value is 2.08 standard deviations greater than the mean, its z-score is simply 2.08. This means the value lies 2.08 standard deviations above the average of the dataset.
In a normal distribution, approximately 68% of scores fall within one standard deviation of the mean (between -1 and +1 standard deviations). About 95% of scores fall within two standard deviations (between -2 and +2 standard deviations). Therefore, the percentage of scores that falls specifically between the mean and -2 to 2 standard deviations is about 95% minus the 50% that is below the mean, resulting in approximately 45%.
All minor deviations occurring with two standard deviations under the Gaussian curve are considered normal. Deviations occurring outside of two standard deviations are considered abnormal.
In a normal distribution, approximately 68% of the population falls within one standard deviation of the mean, and about 95% falls within two standard deviations. Therefore, to find the percentage of the population between one standard deviation below the mean and two standard deviations above the mean, you would calculate 95% (within two standard deviations) minus 34% (the portion below one standard deviation), resulting in approximately 61% of the population.
I'm assuming "genius" means an unusual value (more than two standard deviations) in the right tail. This is (100 - 95.45)/2 = 2.275 percent, approximately. So: 6,575,000,000 * 0.02275 = 149,581,250 geniuses ... not that special, huh?
How many standard deviations is 16.50 from the mean?
2.576 sd
The sum of standard deviations from the mean is the error.
95% is within 2 standard deviations of the mean.
The mean for the WISC, like the WAIS, is 100. The deviations from 100, or standard deviations, are 15.
You can't average means with standard deviations. What are you trying to do with the two sets of data?
The z-score of a value indicates how many standard deviations it is from the mean. If a value is 2.08 standard deviations greater than the mean, its z-score is simply 2.08. This means the value lies 2.08 standard deviations above the average of the dataset.
2 times the standard deviation!
In a normal distribution, approximately 95% of the population falls within 2 standard deviations of the mean. This is known as the 95% rule or the empirical rule. The empirical rule states that within one standard deviation of the mean, about 68% of the population falls, and within two standard deviations, about 95% of the population falls.