Can anyone explain what standard deviation is?
I'm fed up of looking through text books that confuse me rather than help me out.
I know it's GCSE stuff, but i was too busy moaning about how i am never gonna need this and looking at boys instead paying attention to the teacher, and now, ten years later i need to know!
Answers:
I hear your pain. Here's the best way I know to explain it.
A standard deviation is just like a unit of measure. You have that bell curve, right? Okay. All of the points on that bell curve correspond to the number of times that a certain number came up over a range.
with me so far?
1 standard deviation is the 'range' where 68% of the data exists
2 standard deviations is the 'range' where 95% of the data exists
you can do the math (which is likely what is confusing you) but if you think of it as a way to measure how compact or spread out a bell curve is, that helped me.
Standard deviation is a statistical term to describe how far away from the mean (a predetermined average) a certain group of data (scores) will be. It is a confidence interval.
When a person makes a prediction, they say they are 99% (3 Standard Deviations), 95% ( 2 SDs), or 68% (1 SDs) confident that based on the scores they have already seen, certain future scores will occur as they predict.
It's easy to be 99% confident when you use 3 SDs- because that is almost all the scores in the graph.
Confidence intervals can be at the .05 level (p = .05) or harder to prove at the .01 level (they express it as p = .01).
Standard deviations do not have to be just for predictive statistics- they can also be for descriptive statistics, which just show what happened after someone collects scores.
standard deviation is a measure of an average. in statistical analysis, averages are important, as you know. standard deviation tells you how much an average agrees with a set of values. a average, so to speak, can only deviate from a set of values by so much. standard deviation tells you about how much that is. that's why it's more reliable over a large scope of values. across a small set of values, your average is deviates by a margin you can't really predict. as the number of values increases, however, it becomes clear that a good average can't go haywire, but must fall within a certain domain. that domain is the standard deviation of the average.
Standard deviation is one of the measures of variability or spreadness. That is, it is one of the numerical measure that indicate how all the data vary or differ from each other (specifically, from the mean). It is actually the square root of the variance (mean of squared-deviation of all the data from the mean).
The value of the standard deviation indicates the distribution's spreadness. The lower the value of the standard deviation, the more each data cluster around the mean.
We can use it to compare two distribution.
For example, if two distribution have the same mean (average) and distribution A and B has a standard deviation of 5.45 and 2.87, respectively, we can therefore conclude that all the data of distribution B are closer to the mean than in distribution A.
If the standard deviation of a distribution is 0, it can only mean one thing. All the data in the distribution are the same (ex. 5,5,5,5,5,).
Forget all the heavy maths.
SD is just a measure of how 'spead out' your measurements are. Remember that we are talking about a group of measurements (some times called a population), and not just one measurement.
In this group IF the values were all very similar then the SD would be small.
If the values were spread out the SD would have to be larger.
Remember that SD is just a made-up term, we chose to define the SD so that 68% of the values are within 1 standard deviation of the mean.
see the graph at http://en.wikipedia.org/wiki/standard_de.
PS How did the boys turn out? were they worth it?
Without getting into complicated algebra, standard deviation is simply a unitless measure that demonstartes how close the majority of the values in a data set fall in relation to the mean value. The lower the value of standard deviation the closer the majority of values are to the mean and therefore the more consistent the data are.
Hope to have been of help.
It would be useful to know why you're asking. At work I use it often to look at processes. If you have some specification limits, for example minimum 2, maximum 8 and a target value of 5, the standard deviation will tell you how good you process is. Just measure all you parts, processes or whatever readings you are studying. Put then into a spreadsheet such as Excel and use the function key to find the standard deviation. If it is less than 1 in the example then your process is under control. The rule of thumb is if 3 x the standard deviation is less than your allowed tolerance then you are OK.
In Statistical Process Control (SPC) we use a capability figure called Cpk to tell us if our process is in control. It is essentially the same as I have described, but the correct formula is as follows:
Cpk is the smaller of two calculations
Cp upper = (Max spec limit - average)/3 x standard deviation
Cp lower = (average - lower spec limit)/3 x standard deviation
If Cpk is 1.3 or higher then the process is well in control and you can expect everything you make to be within specification. If Cpk is below 1.0 then you can expect rejects outside the specification limits.
I've probably made you completely bored and you're falling asleep, but statistics does this to everyone!
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I know it's GCSE stuff, but i was too busy moaning about how i am never gonna need this and looking at boys instead paying attention to the teacher, and now, ten years later i need to know!
Answers:
I hear your pain. Here's the best way I know to explain it.
A standard deviation is just like a unit of measure. You have that bell curve, right? Okay. All of the points on that bell curve correspond to the number of times that a certain number came up over a range.
with me so far?
1 standard deviation is the 'range' where 68% of the data exists
2 standard deviations is the 'range' where 95% of the data exists
you can do the math (which is likely what is confusing you) but if you think of it as a way to measure how compact or spread out a bell curve is, that helped me.
Standard deviation is a statistical term to describe how far away from the mean (a predetermined average) a certain group of data (scores) will be. It is a confidence interval.
When a person makes a prediction, they say they are 99% (3 Standard Deviations), 95% ( 2 SDs), or 68% (1 SDs) confident that based on the scores they have already seen, certain future scores will occur as they predict.
It's easy to be 99% confident when you use 3 SDs- because that is almost all the scores in the graph.
Confidence intervals can be at the .05 level (p = .05) or harder to prove at the .01 level (they express it as p = .01).
Standard deviations do not have to be just for predictive statistics- they can also be for descriptive statistics, which just show what happened after someone collects scores.
standard deviation is a measure of an average. in statistical analysis, averages are important, as you know. standard deviation tells you how much an average agrees with a set of values. a average, so to speak, can only deviate from a set of values by so much. standard deviation tells you about how much that is. that's why it's more reliable over a large scope of values. across a small set of values, your average is deviates by a margin you can't really predict. as the number of values increases, however, it becomes clear that a good average can't go haywire, but must fall within a certain domain. that domain is the standard deviation of the average.
Standard deviation is one of the measures of variability or spreadness. That is, it is one of the numerical measure that indicate how all the data vary or differ from each other (specifically, from the mean). It is actually the square root of the variance (mean of squared-deviation of all the data from the mean).
The value of the standard deviation indicates the distribution's spreadness. The lower the value of the standard deviation, the more each data cluster around the mean.
We can use it to compare two distribution.
For example, if two distribution have the same mean (average) and distribution A and B has a standard deviation of 5.45 and 2.87, respectively, we can therefore conclude that all the data of distribution B are closer to the mean than in distribution A.
If the standard deviation of a distribution is 0, it can only mean one thing. All the data in the distribution are the same (ex. 5,5,5,5,5,).
Forget all the heavy maths.
SD is just a measure of how 'spead out' your measurements are. Remember that we are talking about a group of measurements (some times called a population), and not just one measurement.
In this group IF the values were all very similar then the SD would be small.
If the values were spread out the SD would have to be larger.
Remember that SD is just a made-up term, we chose to define the SD so that 68% of the values are within 1 standard deviation of the mean.
see the graph at http://en.wikipedia.org/wiki/standard_de.
PS How did the boys turn out? were they worth it?
Without getting into complicated algebra, standard deviation is simply a unitless measure that demonstartes how close the majority of the values in a data set fall in relation to the mean value. The lower the value of standard deviation the closer the majority of values are to the mean and therefore the more consistent the data are.
Hope to have been of help.
It would be useful to know why you're asking. At work I use it often to look at processes. If you have some specification limits, for example minimum 2, maximum 8 and a target value of 5, the standard deviation will tell you how good you process is. Just measure all you parts, processes or whatever readings you are studying. Put then into a spreadsheet such as Excel and use the function key to find the standard deviation. If it is less than 1 in the example then your process is under control. The rule of thumb is if 3 x the standard deviation is less than your allowed tolerance then you are OK.
In Statistical Process Control (SPC) we use a capability figure called Cpk to tell us if our process is in control. It is essentially the same as I have described, but the correct formula is as follows:
Cpk is the smaller of two calculations
Cp upper = (Max spec limit - average)/3 x standard deviation
Cp lower = (average - lower spec limit)/3 x standard deviation
If Cpk is 1.3 or higher then the process is well in control and you can expect everything you make to be within specification. If Cpk is below 1.0 then you can expect rejects outside the specification limits.
I've probably made you completely bored and you're falling asleep, but statistics does this to everyone!
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