Are the following numbers normally distributed? Justify your answer. 0.036238 -0.454 0.031657 -0.79473 -0.09066 0.890987 0.3143 0.887703 0.50879 -1.2039 1.680193 -1.27229 0.564049 -0.14221 1.35349

Question

need answer quick 

Answer 1

Arrange in size order, least to greatest:

-1.27229 -1.2039 -0.79473 -0.454 -0.14221 -0.09066 0.031657 0.036238 0.3143 0.50879 0.564049 0.887703 0.890987 1.35349 1.680193.

median is 0.036238, mean is 0.1539745. The mean is greater than the median so the distribution is skew. In a normal distribution the mean and median are close together. The quartiles are:

Q1=-0.454, Q2=0.036238 (median), Q3=0.887703.

However, the box plot shows that the median and mode are fairly close together and the “whiskers” are of approximately equal length, so the distribution is approximately normal.