Question

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.

Answer 1

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!!