Final answer:
Adding a plant with a height of 174 inches to the dataset of plant heights would significantly increase the mean from 17.31 inches to 28.5 inches; hence, none of the provided options accurately describe the impact on the mean or the range.
Step-by-step explanation:
If another plant with a height of 174 inches is added to the data, the mean height of the plants would be significantly impacted. To calculate the mean, you would sum all the heights of the plants and divide by the number of plants. Let's begin by calculating the original mean before adding the new plant:
The sum of the given plant heights is 12 + 14 + 15 + 15 + 16 + 16 + 16 + 17 + 18 + 19 + 20 + 22 + 25, which equals 225 inches. The number of plants is 13. So, the current mean is 225 inches divided by 13, which equals approximately 17.31 inches.
Now we add the new plant height of 174 inches to get a new total height of 225 + 174, which equals 399 inches. The number of plants is now 14. The new mean is therefore 399 inches divided by 14, which equals 28.5 inches. This significantly alters the mean from its previous value.
None of the provided options are accurate: the mean would not stay the same, and the range would neither increase nor decrease to 17.4 inches. Instead, the range would increase, and the mean would be significantly higher.