Question

Consider the following data : 1.5, 1.5, 1.7, 1.7, 2.1, 2.3

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 x-axis? Separate your answers with a comma

b) 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.

Answer 1

Steps for constructing normal probability plot by hand:

• Arrange your x-values in ascending order.
• Calculate f_i = (i-0.375)/ (n+0.25), where i is the position of the data value in the
  ordered list and n is the number of observations.
• Find the z-score for each f_i
• Plot your x-values on the horizontal axis and the corresponding z-score
  on the vertical axis.

a)

The numerical values (in order) of the first five numbers that would go on the x-axis are 1.5, 1.5, 1.7, 1.7, 2.1.

( which are arrange in ascending order )

b)

Calculate  

where

i = position of the data value

n = number of observation

And find the value of Z from Z-score table corresponding to the probability( area) f _i

position(i)	X i	f i	Z i
1	1.5	0.10	-1.28
2	1.5	0.26	-0.64
3	1.7	0.42	-0.20
4	1.7	0.58	0.20
5	2.1	0.74	0.64
6	2.3	0.90	1.28

Here, Z _i is the value that would go on the Y-axis

Therefore,  the first five numbers that would go on the y-axis are -1.28, -0.64, -0.20, 0.20 and 0.64.