Is a standard deviation of 14.889 considered high, low or moderate?

Question

the mean score is 108.447, my score is 124 and total samples is 5.42 million. I'm just not clear on what standard deviation means and whether 14.889 is considered small or large.

Both Blog, and James helped me to understand the concept. I thank you both. I haven't figured out how to divide the best answer, so I'll have to be random.

Answer 1

It is irrelevant whether the standard deviation is high, low or moderate for your evaluation of where in the normal distribution stands under the probability distribution or bell curve. Still, how spread or bunched up a distribution is, is known as kurtosis. Bunched up is leftikurtic, spread out is platikurtic (the spelling might be off on those).
The standard deviation is how spread out a distribution is. 68 percent of all scores fall between, + or minus 1 standard deviation from the mean.About 95% of scores fall + or minus 2 standard deviations from the mean. 99% fall + or minus 3 standard deviations from the mean.
For your score of 124, to find where it stands in the distribution you simply
124-108.447/ 14.889 = 1.0446 which puts you at the 85th percentile. You get that number from a z-table by looking up 1.0446 and finding the associated probability of .8508
i hope this helps.

Answer 2

The standard deviation is a measure of how far your data varies from the mean. It is technically the square root of your variance. Hence, higher variance (around the mean), a higher standard deviation. For your score of 124, it is about 1 standard deviation above the mean, which places you at
68%/2+50=84th percentile. That is, you scored better than 84%, but worse than about 16%.

However, the standard deviation depends in part n the sample size, because we take the ratio of the sum of squared deviations from the mean OVER N-1. (That's the variance, the standard deviation is the square root of that).

The standard deviation is used in calculating sample statistics. For example, we expect that 68% of all your data points will be +/- 1 standard deviation from the mean, 95% within +/- 2 s.d. and 99% within 3 standard deviations. It gives you an idea both of how your data is dispersed, and how much of that data lies in any region.

14.889 does not seem too high, but make sure you calculated it correctly, since your very large sample size makes me feel it may actually be smaller than that. If it is correct, then you can say 95% of all your data is between -(108.447-2*14.889) and (108.447+2*14.889), or [78.669,138.225]

Answer 3

The question is pretty meaningless.

Standard deviation is a measure -- derived from looking at all the scores together -- of how remarkable SPECIFIC scores are.

In this case, 124 is about 1 standard deviation from the mean, so it's a pretty unremarkable score.