I understand standard deviation a bit but not fully so kindly someone explain two standard deviation.
In: 5
There’s a way to model how data is distributed called a normal distribution or Gaussian distribution. The x axis is the value and the y axis is how likely that is. There’s a peak at the mean value (ie the mean is the most likely) and the likelihood decreases as you get further away (how quickly depends on the standard deviation). You can use this to determine how likely a value is. 68% of data points fall within +- one standard deviation of the mean. 95% of the points fall within +- 2 standard deviations. So when someone uses two standard deviations, they mean 95% chance of the data falling within 2 standard deviations of the mean.
According to one survey, American adult males have an average height of 70 inches and a standard deviation of 2.66 inches. That means anyone of height 75.33 inches or above is two standard deviations above the mean (70 + 2.66 + 2.66). In a perfect bell curve, 2.3% of all samples are two std. devs. above the mean, 2.3% of all samples are two std. devs. below the mean, and 95.4% of all samples are within two std. devs. of the mean.
The idea being “when is a value big or small”.
If I put two arrows a meter apart is that a big difference or a little one? It depends. We need context. That might be something like how far away you are from the target.
Mathematically, the SD provides that context.
Do you usually shoot arrows which are separated by a meter?
Let me put that in math-speak: Is it “standard” for you to have arrows which “deviate” by a meter?
For some of the more common distributions, the majority (~65%) is within 1 SD and the vast majority (over 95%) of the data is within 2 SDs. So a value within two Standard deviations is very common.
So if the arrows are more than 2 SDs apart, that is likely (though not guaranteed) to be unusual and not just happenstance.
The idea being “when is a value big or small”.
If I put two arrows a meter apart is that a big difference or a little one? It depends. We need context. That might be something like how far away you are from the target.
Mathematically, the SD provides that context.
Do you usually shoot arrows which are separated by a meter?
Let me put that in math-speak: Is it “standard” for you to have arrows which “deviate” by a meter?
For some of the more common distributions, the majority (~65%) is within 1 SD and the vast majority (over 95%) of the data is within 2 SDs. So a value within two Standard deviations is very common.
So if the arrows are more than 2 SDs apart, that is likely (though not guaranteed) to be unusual and not just happenstance.
The idea being “when is a value big or small”.
If I put two arrows a meter apart is that a big difference or a little one? It depends. We need context. That might be something like how far away you are from the target.
Mathematically, the SD provides that context.
Do you usually shoot arrows which are separated by a meter?
Let me put that in math-speak: Is it “standard” for you to have arrows which “deviate” by a meter?
For some of the more common distributions, the majority (~65%) is within 1 SD and the vast majority (over 95%) of the data is within 2 SDs. So a value within two Standard deviations is very common.
So if the arrows are more than 2 SDs apart, that is likely (though not guaranteed) to be unusual and not just happenstance.
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