Determining the distribution for a sample data set

Question

I have a sample data set of heights of students where

X = (1.65,1.55,1.78,1.43,1.69)

and I'm required to fit a normal distribution to the data X.

The thing I'm confused now is, should i use a Gaussian Distribution or a Poisson Distribution? I know that Poisson is used mainly for the purpose of counting occurrences but i also discovered that the normal distribution is the Gaussian Distribution but I'm not really clear about it.

Is the Gaussian Distribution the only distribution that is considered normal distribution?

Answer 1

Normal distribution is the same as Gaussian distribution. To fit your data to a normal distribution, i.e. find the parameters of Gaussian (Normal) distribution just put:

$$ \hat{\mu} = \frac{X_1 + \dots + X_5} {5}, \quad \hat{\sigma}^2 = \frac{(X_1 - \hat{\mu})^2 + \dots + (X_5 - \hat{\mu})^2}{4}. $$ Then, your fitted distribution will be $\mathcal{N}\left(\hat{\mu}, \hat{\sigma}^2\right)$.

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Note that we divided by $4$ (in second equation above), which, in general case, is $n - 1$, since this estimate for $\hat{\sigma}^2$ is the unbiased one.