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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

(1 point)
Responses

Fertilizers A and B are both ineffective, because there is no difference in the ranges of the weights of the potatoes.
Fertilizers A and B are both ineffective, because there is no difference in the ranges of the weights of the potatoes.

Fertilizers A and B are equally effective, because the ranges of the weights of the potatoes are the same.
Fertilizers A and B are equally effective, because the ranges of the weights of the potatoes are the same.

Fertilizer B is generally more effective, because the mean and median weights of the potatoes that were treated with it are higher.
Fertilizer B is generally more effective, because the mean and median weights of the potatoes that were treated with it are higher.

Fertilizer A is generally more effective, because the mean and median weights of the potatoes treated with it are higher.

:)

1 answer

To determine which fertilizer is generally more effective, we can calculate the mean and median weights of the potatoes for both fertilizers.

Fertilizer A weights: 27, 20, 16, 18, 22, 19, 23, 21, 17, 19

  1. Mean of Fertilizer A: \[ \text{Mean} = \frac{27 + 20 + 16 + 18 + 22 + 19 + 23 + 21 + 17 + 19}{10} = \frac{ 27 + 20 + 16 + 18 + 22 + 19 + 23 + 21 + 17 + 19 }{10} = \frac{ 202 }{10} = 20.2 \text{ kg} \]

  2. Median of Fertilizer A:

    • Sorted weights: 16, 17, 18, 19, 19, 20, 21, 22, 23, 27
    • Median (average of the 5th and 6th numbers in sorted order): \[ \text{Median} = \frac{19 + 20}{2} = 19.5 \text{ kg} \]

Fertilizer B weights: 28, 19, 18, 21, 24, 20, 25, 27, 29, 21

  1. Mean of Fertilizer B: \[ \text{Mean} = \frac{28 + 19 + 18 + 21 + 24 + 20 + 25 + 27 + 29 + 21}{10} = \frac{ 212 }{10} = 21.2 \text{ kg} \]

  2. Median of Fertilizer B:

    • Sorted weights: 18, 19, 20, 21, 21, 24, 25, 27, 28, 29
    • Median (average of the 5th and 6th numbers in sorted order): \[ \text{Median} = \frac{21 + 24}{2} = 22.5 \text{ kg} \]

Comparison:

  • Mean of Fertilizer A: 20.2 kg
  • Median of Fertilizer A: 19.5 kg
  • Mean of Fertilizer B: 21.2 kg
  • Median of Fertilizer B: 22.5 kg

Since both the mean and median weights of potatoes for Fertilizer B are higher than those for Fertilizer A, we conclude:

Fertilizer B is generally more effective, because the mean and median weights of the potatoes that were treated with it are higher.