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Glen_b
Glen_b
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Conceptual understanding of standard deviation vs average distance from the mean

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Andy
Andy
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I always understood standard deviation to be the average distance of the observations from the mean. But when I generated a standard normal distribution N(0,1) with n = 1,000,000 in Excel, and took the average of all negative observations and the average of all positive observations, I got around -0.80 and +0.80 respectively, when I would have expected to get -1 and +1. The empirical results indicate that the average distance of an observation from EV = 0 is 0.8, yet the standard deviation is 1.

How do I reconcile this conceptually for my own understanding?

Thanks.

I always understood standard deviation to be the average distance of the observations from the mean. But when I generated a standard normal distribution N(0,1) with n = 1,000,000 in Excel, and took the average of all negative observations and the average of all positive observations, I got around -0.80 and +0.80 respectively, when I would have expected to get -1 and +1. The empirical results indicate that the average distance of an observation from EV = 0 is 0.8, yet the standard deviation is 1.

How do I reconcile this conceptually for my own understanding?

Thanks.

I always understood standard deviation to be the average distance of the observations from the mean. But when I generated a standard normal distribution N(0,1) with n = 1,000,000 in Excel, and took the average of all negative observations and the average of all positive observations, I got around -0.80 and +0.80 respectively, when I would have expected to get -1 and +1. The empirical results indicate that the average distance of an observation from EV = 0 is 0.8, yet the standard deviation is 1.

How do I reconcile this conceptually for my own understanding?

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Jon
Jon
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Conceptual understanding of standard deviation

I always understood standard deviation to be the average distance of the observations from the mean. But when I generated a standard normal distribution N(0,1) with n = 1,000,000 in Excel, and took the average of all negative observations and the average of all positive observations, I got around -0.80 and +0.80 respectively, when I would have expected to get -1 and +1. The empirical results indicate that the average distance of an observation from EV = 0 is 0.8, yet the standard deviation is 1.

How do I reconcile this conceptually for my own understanding?

Thanks.