A tree was 8 inches tall when it was planted. The graph above shows the height of the tree at the end of each of the first 4 months after it was planted. What was the tree's average (arithmetic mean) monthly increase in height during these 4 months?

Rationale

The tree's average monthly increase in height during these 4 months was 6 1/4 inches.

To determine the average monthly increase, we first need to find the final height of the tree after 4 months, which can then be compared to the initial height of 8 inches. The average increase is calculated by subtracting the initial height from the final height and dividing by the number of months.

A (5 1/4 in) YOUR ANSWER

This option suggests a monthly increase that is too low. If the total height increase were 5 1/4 inches over 4 months, the final height would only be 13 1/4 inches, which does not align with the data presented in the graph.

B (6 1/4 in) CORRECT

This choice accurately reflects the average monthly increase in height. If the tree started at 8 inches and reached a total height of 32 1/4 inches after 4 months, the total increase would be 24 1/4 inches. Dividing this by 4 months results in a monthly increase of 6 1/4 inches.

C (6 3/4 in) YOUR ANSWER

Selecting this option implies a greater monthly increase than what was calculated. A monthly increase of 6 3/4 inches would lead to a total increase of 27 inches over 4 months, resulting in a final height of 35 inches, which is not supported by the graph.

D (7 1/4 in) YOUR ANSWER

This choice also indicates an excessively high average monthly increase. A monthly growth of 7 1/4 inches would yield a total increase of 29 inches over 4 months, leading to a final height of 37 inches, which does not correspond to the data.

E (7 3/4 in) YOUR ANSWER

This option suggests an even larger average increase, which is not feasible. A monthly increase of 7 3/4 inches would result in a total height of 39 inches after 4 months, again contradicting the graph's data.

Conclusion

The average monthly increase in height of the tree, calculated from its initial and final heights, confirms that the correct answer is 6 1/4 inches. Each incorrect option suggests a different total height that does not match the graph, illustrating the importance of accurate interpretation of data when calculating averages.

A tree was 8 inches tall when it was planted. The graph above shows the height of the tree at the end of each of the first 4 months after it was planted. What was the tree's average (arithmetic mean) monthly increase in height during these 4 months?

The tree's average monthly increase in height during these 4 months was 6 1/4 inches.

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