Question

Permeability of sandstone during weathering.Natural stone, such as sandstone, is a popular building construction material. An experiment was carried out to better understand the decay properties of sandstone when exposed to the weather (Geographical Analysis,Vol. 42, 2010). Blocks of sandstone were cut into 300 equal-sized slices and the slices randomly divided into three groups of 100 slices each. Slices in Group A were not exposed to any type of weathering; slices in Group B were repeatedly sprayed with a 10% salt solution (to simulate wetting by driven rain) under temperate conditions; and slices in Group C were soaked in a 10% salt solution and then dried (to simulate blocks of sandstone exposed during a wet winter and dried during a hot summer). All sandstone slices were then tested for permeability, measured in milliDarcies (mD). These permeability values measure pressure decay as a function of time. The data for the study (simulated) are saved in the STONEfile. Measures of central tendency for the permeability measurements of each sandstone group are displayed in the accompanying Minitab printout.

Descriptive Statistics: PermA, PermB, PermC
Variable	N	Mean	Median	Mode	N for Mode
PermA	100	73.62	70.45	59.9, 60, 60.1, 60.4	2
PermB	100	128.54	139.30	146.4, 146.6, 147.9, 148.3	3
PermC	100	83.07	78.65	70.9	3
The data contain atleast 5 mode value. Only the smallest 4 are shown

a.Interpret the mean and median of the permeability measurements for Group A sandstone slices.

b.Interpret the mean and median of the permeability measurements for Group B sandstone slices.

c.Interpret the mean and median of the permeability measurements for Group C sandstone slices.

d.Interpret the mode of the permeability measurements for Group C sandstone slices.

e.The lower the permeability value, the slower the pressure decay in the sandstone over time. Which type of weathering (type B or type C) appears to result in faster decay?

Short answer

a. Mean = 73.62, Median = 70.45

b. Mean = 128.54, Median = 139.30

c. Mean = 83.07, Median = 78.65

d. Mode = 70.9

e. Type B

Step-by-step solution

Interpreting the mean and median of the permeability measurements for Group A 

The average permeability for Group A of sandstone slices is 73.62 mD. When the sandstone is not exposed to any weathering, its permeability level is around 73.62 mD over time.

The median for Group A is 70.45 mD. That implies 50% of sandstone slices in no weathering condition will have permeability levels below 70.45 mD and, 50% will have more than that.

Understanding the mean and median of the permeability measurements for Group B

The mean here is 128.54 mD. Therefore we know that when the sandstone is exposed to the conditions in Group B, the average rate of permeability is 128.54 mD.

As the median permeability for Group B is 139.30 mD, it indicates that half slices will have less permeability than 139.30 mD and half have permeability more than tha

Illustrating the meaning of mean and median for the permeability measurements of Group C

83.07 mD is the mean permeability in Group C. Indicating the average rate of permeability in weather conditions created for Group C.

The median being 78.65 mD indicates that 50% slices may have permeability levels above and 50% may have permeability levels below 78.65 mD.

Explaining the mode of the permeability measurements for Group C 

70.9 mD is the mode because it was repeated a maximum number of times (3) in the group. We can infer from this that when rocks are exposed to weather conditions, such as in Group C, the most likely permeability rate will be 70.9 mD.

Determining which type of weathering leads to faster decay

Type B weathering appears in faster decay because the mean permeability value is higher for type B. Also, the mode values are higher than type C, indicating that the most common permeability values are higher and that more stones under type B weathering are likely to have higher values.