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23 Sep 2025, 09:02
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The median hardness of all 12 minerals belongs to a Feldspar-type mineral.: Yes
The average density of the Mica-type minerals is greater than the average density of the Quartz-type minerals.: Yes
The range of hardness values among the Quartz-type minerals is greater than the range of hardness values among the Feldspar-type minerals.: No
The table shows physical characteristics of several minerals that have been sorted into three categories: Quartz-type, Feldspar-type, and Mica-type.
For each of the following statements, select Yes if it must be true based only on the information in the table; otherwise select No.
| Mineral | Color | Hardness (Mohs scale) | Crystal form | Density (g/cm3) | Category |
|---|---|---|---|---|---|
| 1 | Clear | 7 | Hexagonal | 2.6 | Quartz-type |
| 2 | Pink | 6 | Monoclinic | 2.5 | Feldspar-type |
| 3 | Black | 3 | Sheet-like | 2.8 | Mica-type |
| 4 | White | 6 | Triclinic | 2.7 | Feldspar-type |
| 5 | Gray | 7 | Hexagonal | 2.6 | Quartz-type |
| 6 | Brown | 2 | Sheet-like | 2.9 | Mica-type |
| 7 | Yellow | 5 | Triclinic | 2.5 | Feldspar-type |
| 8 | Blue | 8 | Hexagonal | 2.7 | Quartz-type |
| 9 | Green | 4 | Sheet-like | 3.0 | Mica-type |
| 10 | Orange | 6 | Monoclinic | 2.6 | Feldspar-type |
| 11 | Violet | 7 | Hexagonal | 2.65 | Quartz-type |
| 12 | Silver | 3 | Sheet-like | 2.85 | Mica-type |
For each of the following statements, select Yes if it must be true based only on the information in the table; otherwise select No.
| Yes | No | |
| The median hardness of all 12 minerals belongs to a Feldspar-type mineral. | ||
| The average density of the Mica-type minerals is greater than the average density of the Quartz-type minerals. | ||
| The range of hardness values among the Quartz-type minerals is greater than the range of hardness values among the Feldspar-type minerals. |
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Official Answer
The median hardness of all 12 minerals belongs to a Feldspar-type mineral.: Yes
The average density of the Mica-type minerals is greater than the average density of the Quartz-type minerals.: Yes
The range of hardness values among the Quartz-type minerals is greater than the range of hardness values among the Feldspar-type minerals.: No
23 Sep 2025, 09:02
Kudos
Bookmarks
Official Solution:
• The median hardness of all 12 minerals belongs to a Feldspar-type mineral.
To determine the median hardness, we sort all the hardness values from lowest to highest. With 12 minerals, the median is the average of the 6th and 7th values in the list. Both of these values correspond to hardness 6, which is associated with Feldspar-type minerals.
Answer: Yes
• The average density of the Mica-type minerals is greater than the average density of the Quartz-type minerals.
We should calculate the average density for the Quartz-type minerals and then compare it with the average density for the Mica-type minerals. Adding the densities for the Quartz-type and dividing by 4 gives a value a little above 2.6. Doing the same for the Mica-type gives a value closer to 2.9. Since the latter is clearly higher, the Mica-type minerals have the greater average density.
Answer: Yes
• The range of hardness values among the Quartz-type minerals is greater than the range of hardness values among the Feldspar-type minerals.
Range is defined as the difference between the largest and smallest value in a set. For the Quartz-type minerals, the hardness values go from 7 to 8, so the range is 1. For the Feldspar-type minerals, the hardness values go from 5 to 6, so the range is also 1. Because they are equal, the range for Quartz-type is not greater.
Answer: No
Correct answer:
The median hardness of all 12 minerals belongs to a Feldspar-type mineral. "Yes"
The average density of the Mica-type minerals is greater than the average density of the Quartz-type minerals. "Yes"
The range of hardness values among the Quartz-type minerals is greater than the range of hardness values among the Feldspar-type minerals. "No"
Bunuel
• The median hardness of all 12 minerals belongs to a Feldspar-type mineral.
To determine the median hardness, we sort all the hardness values from lowest to highest. With 12 minerals, the median is the average of the 6th and 7th values in the list. Both of these values correspond to hardness 6, which is associated with Feldspar-type minerals.
Answer: Yes
• The average density of the Mica-type minerals is greater than the average density of the Quartz-type minerals.
We should calculate the average density for the Quartz-type minerals and then compare it with the average density for the Mica-type minerals. Adding the densities for the Quartz-type and dividing by 4 gives a value a little above 2.6. Doing the same for the Mica-type gives a value closer to 2.9. Since the latter is clearly higher, the Mica-type minerals have the greater average density.
Answer: Yes
• The range of hardness values among the Quartz-type minerals is greater than the range of hardness values among the Feldspar-type minerals.
Range is defined as the difference between the largest and smallest value in a set. For the Quartz-type minerals, the hardness values go from 7 to 8, so the range is 1. For the Feldspar-type minerals, the hardness values go from 5 to 6, so the range is also 1. Because they are equal, the range for Quartz-type is not greater.
Answer: No
Correct answer:
The median hardness of all 12 minerals belongs to a Feldspar-type mineral. "Yes"
The average density of the Mica-type minerals is greater than the average density of the Quartz-type minerals. "Yes"
The range of hardness values among the Quartz-type minerals is greater than the range of hardness values among the Feldspar-type minerals. "No"
