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Two fertilizers are applied to randomly selected potato plants. After several weeks, the potatoes are weighed. The weights in kilograms are as follows. Which fertilizer is generally more effective?
Fertilizer A: 27, 20, 16, 18, 22, 19, 23, 21, 17, 19
Fertilizer B: 28, 19, 18, 21, 24, 20, 25, 27, 29, 21
A. Fertilizers A and B are both ineffective, because there is no difference in the ranges of the weights of the potatoes.
B. Fertilizer A is generally more effective, because the mean and median weights of the potatoes treated with it are higher.
C. Fertilizers A and B are equally effective, because the ranges of the weights of the potatoes are the same.
D. Fertilizer B is generally more effective, because the mean and median weights of the potatoes that were treated with it are higher.
To determine which fertilizer is generally more effective, we need to analyze the given data.
First, let's calculate the ranges of the weights for each fertilizer:
Fertilizer A: range = maximum value - minimum value = 27 - 16 = 11 kg
Fertilizer B: range = maximum value - minimum value = 29 - 18 = 11 kg
The ranges for both fertilizers are the same, so option C can be eliminated.
Next, let's compare the mean and median weights for each fertilizer:
Fertilizer A: mean = (27 + 20 + 16 + 18 + 22 + 19 + 23 + 21 + 17 + 19) / 10 = 20.2 kg
median = the middle value when the weights are arranged in ascending order = 19 kg
Fertilizer B: mean = (28 + 19 + 18 + 21 + 24 + 20 + 25 + 27 + 29 + 21) / 10 = 22.2 kg
median = the middle value when the weights are arranged in ascending order = 21 kg
The mean and the median weights of the potatoes treated with Fertilizer B are higher than those treated with Fertilizer A. Therefore, option D can be eliminated.
Based on the analysis, we can conclude that Fertilizer B is generally more effective, as the mean and median weights of the potatoes treated with it are higher than the weights of the potatoes treated with Fertilizer A. Therefore, the correct answer is option D.