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Question: Permeability of sandstone during weathering.Refer to the Geographical Analysis(Vol. 42, 2010) study of the decay properties of sandstone when exposed to the weather, Exercise 2.47 (p. 96). Recall that slices of sandstone blocks were tested for permeability under three conditions: no exposure to any type of weathering (A), repeatedly sprayed with a 10% salt solution (B), and soaked in a 10% salt solution and dried (C). Measures of variation for the permeability measurements (mV) of each sandstone group are displayed in the accompanying Minitab printout.

Descriptive Statistics: PermA, PermB, PermC
Variable	N	StDev.	Variance	Minimum	Maximum	Range
PermA	100	14.48	209.53	55.20	122.40	67.20
PermB	100	21.97	482.75	50.40	150.00	99.60
PermC	100	20.05	401.94	52.20	129.00	76.80

a.Find the range of the permeability measurements for Group A sandstone slices. Verify its value using the minimum and maximum values shown on the printout.

b.Find the standard deviation of the permeability measurements for Group A sandstone slices. Verify its value using the variance shown on the printout.

c.Which condition (A, B, or C) has the more variable permeability data?

Step by step solution

01

Finding the Range and Verifying its value 

The range of permeability measurements for Group A is 67.20.

The minimum value is 55.20 and the maximum value is 122.40.

Therefore,

$$\begin{gathered} \mathbf{Range}\mathbf{=}\mathbf{Max}\mathbf{-}\mathbf{Min} \\ \mathbf{=}\mathbf{122}\mathbf{.}\mathbf{40}\mathbf{-}\mathbf{55}\mathbf{.}\mathbf{20} \\ \mathbf{=}\mathbf{67}\mathbf{.}\mathbf{20} \end{gathered}$$

02

Looking for the standard deviation and checking its value

The standard deviation of permeability measurements for Group A is 14.48.

To check the value, we know that Standard deviation is the square root of variance and the variance is 209.53.

Therefore,

$$\begin{gathered} \mathbf{StDev}\mathbf{=}\sqrt{\mathbf{Variance}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\sqrt{\mathbf{209}\mathbf{.}\mathbf{53}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{14}\mathbf{.}\mathbf{48} \end{gathered}$$

03

Identifying the condition that has the most variable permeability data

As the values of all measures of variability (standard deviation, variance and range) are high for condition B, we can easily say that condition B has the most variable permeability data.

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