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The normal distribution is characterized by the bell shaped curve.

My question is that which curve is bell shaped in the normal distribution? Is it the frequency histogram, the relative frequency curve, or the PDF that is bell shaped?

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  • $\begingroup$ The density function is bell shaped $\endgroup$
    – Chaos
    Jul 1 '20 at 14:20
  • $\begingroup$ Then why I do see that it is the frequency histogram in some places? $\endgroup$
    – Positron12
    Jul 1 '20 at 14:21
  • $\begingroup$ From Wikipedia : "Histograms give a rough sense of the density of the underlying distribution of the data." $\endgroup$
    – Chaos
    Jul 1 '20 at 14:31
  • $\begingroup$ en.m.wikipedia.org/wiki/…. $\endgroup$
    – Chaos
    Jul 1 '20 at 14:31
  • $\begingroup$ Thanks. What about the relative frequency curve? $\endgroup$
    – Positron12
    Jul 1 '20 at 14:33
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The normal distribution is continuous - it can take any value in the real numbers. Any value it takes has a zero probability of being exactly repeated - frequencies will be 0 or 1. So it has a probability density function, not a freqency curve.

A frequency histogram represents discrete values which may occur more than once. That might be for a discrete distribution (e.g. the Binomial) which is approximately normal, or for sample data from a normal distribution that has been grouped into ranges giving frequencies greater than 1. So when you see a freqency histogram in the classic bell shape, you're seeing something that approximates to, or derives from, a normal distribution.

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