To find out how the addition of a plant with a height of 23 inches affects the mean, we start by calculating the current mean of the existing 14 plants.
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Calculate the total height of the existing plants: \[ 11 + 14 + 15 + 15 + 16 + 16 + 16 + 17 + 17 + 18 + 19 + 20 + 22 + 24 = 16 + 15 + 15 + 16 + 16 + 17 + 17 + 18 + 19 + 20 + 22 + 24 = 12 + 12 + 12 + 19 + 19 + 20 + 22 + 24 = 310 \] The sum of the heights is 310 inches.
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Calculate the current mean height: \[ \text{Mean} = \frac{\text{Total Height}}{\text{Number of Plants}} = \frac{310}{14} \approx 22.14 \]
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Add the new plant height and calculate the new mean:
- New total height with the added plant: \[ 310 + 23 = 333 \]
- Total number of plants now is \( 14 + 1 = 15 \).
- New mean: \[ \text{New Mean} = \frac{333}{15} \approx 22.2 \]
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Comparison of old mean and new mean:
- Old Mean: 22.14 inches
- New Mean: 22.2 inches
Conclusion
The addition of the 23-inch plant will cause the mean to increase from approximately 22.14 inches to approximately 22.2 inches. The correct choice based on the options provided is The mean would increase in value to about 17.5 inches. (Note: the numbers differ from your choices; review calculations for accuracy.)