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In a normal distribution ,as far as I know distribution represents frequency of sth.But then how come normal distribution y-axis becomes

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If distribution y-axis doesnt represent frequency, the what is central limit theorem.The central limit theorem y-axis represents the frequency of mean samples.Shouldnt it represent the above formula to satisfy a normal distribution

OTStats
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Fasty
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    What? Normal distribution doesn't represent frequency on the y-axis, but rather density. Frequency only works for discrete distributions. CLT is unrelated here. – user2974951 Sep 18 '19 at 12:40
  • The central limit theorem says, the sample means frequncy if plotted will follow normal distrbution.So y-axis represents no of samples ryt? or does it represent the above formula? – Fasty Sep 18 '19 at 12:41
  • No, we use the CLT to estimate the distribution of the mean. But the mean is a continuous variable and so will also be distributed on the real line ${\rm I!R}$. Which means you will also get a density, not frequency. – user2974951 Sep 18 '19 at 12:50
  • But central limit theorem says we plot frequency in y-axis ryt? – Fasty Sep 18 '19 at 12:54
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    You really need to understand probability densities and distribution functions before you can understand what the central limit theorem says – CloseToC Sep 18 '19 at 12:56
  • There are two distinct questions here, so I have provided links to threads that answer each one separately. There are many other posts on this site that speak to the issues raised in this question: consider conducting a search. – whuber Sep 18 '19 at 13:52

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As you can see from the definition of the normal density, it is not dimension-less, but its measurment unit (dimension in the physical meaning) is the same as that of $1/\sigma$ which in turn is the same dimension as that of $1/x$. Integrating over $f(x)$ yields a dimensionless quantity: the probability of the region of integration.

The y-axis is thus "probabilty per measurement unit of x". This holds for every probability density, not only the normal density.

cdalitz
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