# what do you mean by two standard deviation?

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I understand standard deviation a bit but not fully so kindly someone explain two standard deviation.

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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.

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.

“Standard Deviation” is a measure of how spread apart data is: all other things being equal, a data set with a smaller standard deviation is closer to each other; while a data set with larger standard deviation is more spread out.

What this is good for is measuring how far off the “norm” something is – which allows you to compare different things. For example, if I want to look at who is the best athlete right now, I need to compare players in a lot of different games; so my measure is going to be how many standard deviations above average each athlete is. This allows me to compare soccer players to baseball players to American football players to swimmers, and so on.

“Two standard deviations” means two of these standard units of variation.

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.

“Standard Deviation” is a measure of how spread apart data is: all other things being equal, a data set with a smaller standard deviation is closer to each other; while a data set with larger standard deviation is more spread out.

What this is good for is measuring how far off the “norm” something is – which allows you to compare different things. For example, if I want to look at who is the best athlete right now, I need to compare players in a lot of different games; so my measure is going to be how many standard deviations above average each athlete is. This allows me to compare soccer players to baseball players to American football players to swimmers, and so on.

“Two standard deviations” means two of these standard units of variation.