Is it possible to figure out, WITHOUT THE USE OF GRAPH, if the sample of a...

Is it possible to figure out, WITHOUT THE USE OF GRAPH, if the sample of a data comes from Normal Distribution? If it is possible that by doing some kind of mathematical calculation we can find if a distribution is normal or not? If you could share some example(s), that would be great.

Expert Solution

Yes we can.,

If we have the data we need to find the men of the data(Sigma Xi/n) and std deviation of the data (i.e. sqt(sigma (Xi-Xbar)^2/n))

Once we find the Mean and sd of the data we need to find the following

1)Mean + sd & Mean - sd : If minimum 68% of the observations fall in this region &

2) Mean + 2*sd & Mean -2*sd If minimum 95.5% of the observations fall in this region &

3) Mean + 3*sd *Mean - 3*sd If minimum 99.7% of the observations fall in this region

So if the above 3 conditions are satisfied then we can say that the distribution is normal without the help of graphs.

example.,

Say the mean is 0 and sd =1

then min 68% of the observations have to be between -1 to 1&

min 95.5% of the observations have to be between -2 to 2 &

min 99.7% of the observations have to be between -3 to 3

to confirm normal distribution without graphs

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!

orchestra answered 1 year ago

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