Question

Consider the following data. 21, 21, 37, 33, 38, 21, 37

(a)	If you were to construct a normal probability plot by hand for the above data what are the numerical values (in order) of the first five numbers that would go on the y-axis? Separate your answers with a comma. (use Z table)

Answer 1

Dear student, please comment in the case of any doubt and I would love to clarify it.

Firstly, I have solved it on Excel for reference, but I will solve it on paper as well.

For drawing the graph, we need to calculate the corresponding z-value for the X-values(given values). For z-score, we need to calculate probabilities, the formula for which is-

f = (i - 0.375) / (n + 0.25)

where f is the probability, i is the position of the element, n is the number of observations.

so calculate it for the first element -

f = (1-0.375) / (7+0.25) = 0.086207

And in the same way, we can calculate for other values of X.

For calculating z-score of it, we need to use the z-table, for 0.086207, z-score comes out to be -1.36449.

In the same way, calculate for others.

The first five corresponding values for X-values are-

-1.36449

-0.75829

-0.35293

0

0.352934