I’ve been looking at Statistics in my free time and what exactly does standard deviation is useful for and/or how can I extract meaningful data by using SD and what conclusion can I derive from said data?
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The “Standard Deviation” is the normal range you could expect a given set of values to fall between in a dataset. It’s to make it such that you know what you’re looking at. And also helps for outlier analysis.
Shoot one shot with a regular shotgun on a paper target. Saw the barell off and shoot again. The average distance from the center will differ. That difference will matter.
The mean is the average of your set of data. Each data point in a set has a small difference or deviation between it and the mean. The standard deviation is the average of these small differences. It helps tell you how precise or tightly clustered your data is around the mean with a small value being more precise than a large one.
If the average female height is 62 inches and the standard deviation is 3, one standard deviation is +/- 3 in either direction and two standard deviations are +/- 6 in either direction. We use the phrasing within one/two/X# standard deviations to scale probability calculations like Z scores…which is another lecture.
Hope this helped.
I recommend stat info from here. It’s helped me in the past
https://www.statology.org/find-probability-given-mean-and-standard-deviation/
It’s simply a measure of how close sample values are to their mean. If all sample values are the same, the standard deviation would be zero. If they’re all close to the mean, the SD will be small. If the values are widely spread the SD will be correspondingly large.
When the standard deviation is too large, then essentially the data isn’t valuable.
The smaller the standard deviation, the stronger the trend is.
Standard deviation measures how far away the data typically is from the mean. A larger standard deviation signifies that the data points are very spread out, while a smaller standard deviation signifies that the data are mostly near the mean.
A slightly more intuitive way to measure the spread of data is to use the “absolute mean deviation,” which is actually the mean of the deviations. You take each data point, calculate the distance it is from the mean, then average out those distances by calculating the mean of them. This will usually be close in value to the standard deviation, but the standard deviation is more commonly used because calculating it is “nicer” mathematically. That is, the standard deviation plays nicely with calculus techniques.
Lots of great responses on what standard deviation is, so I thought I would add another way it is useful… if you have a normal distribution (also called Gaussian distribution, which lots of random things tend towards a normal distribution) then the standard deviation can tell you the probability of where values lie. So for example, if you know something has a normal distribution and a mean of 4 with a standard deviation of 1, then there is a 68% chance a random value in that distribution would be between 3 and 5 (mean +/- stdev). 95% would be between 2 and 6 and 99.7% would be between 1 and 7.
Working backwards from this, you could also figure out how likely something is if you know it is a normal distribution and you know the mean and standard deviation. So take the SAT for example, the test is made to have a scores of 200-800 on each section with a normal distribution having a mean of 500 and a standard deviation of 100. You happened to get a 710 and wonder how many others did as well. Well as above, 95% would be between 2 standard deviations of the mean, so 300-700. And being a normal distribution it would also mean that exactly half of the ones not in that 95% would be higher than 700 and half will be lower than 300. So by getting higher than 700, you are in the top 2.5% of test takers.
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