For a certain location in the Northern Hemisphere, the graph shows both the average (arithmetic mean) number of inches of...

Owning The Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

• July is unique: Rain increases from June to July, but runoff decreases — the only such month in the dataset.
• Runoff is highly seasonal: it is greatest late winter/early spring when rain and saturated ground coincide, and lowest in summer when vegetation reduces water flow to the river.
• The largest difference between rain and runoff is in summer (notably July), showing how much rain is retained by soil and plants instead of flowing out as runoff.

Step-by-Step Solution

Question 1: Identifying the Unique Month Where Rain Increases and Runoff Decreases Compared to the Previous Month

Complete Statement:

As compared with the previous month, the only month with a greater average amount of rain and a lesser average amount of runoff is ______

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: As compared with the previous month
  • Meaning: We need to look for changes from one month to the next, rather than absolute values.
  • Relation to Chart: This requires directly comparing rainfall and runoff in adjacent months in the chart.
  • Important Implications: Sets up a month-to-month comparison rather than considering each month independently.
• Statement Breakdown 2:
  • Key Phrase: greater average amount of rain
  • Meaning: The rain value in the target month must be higher than in the previous month.
  • Relation to Chart: Find months where the rain bar is taller than the previous month's.
  • Important Implications: Narrows down months to when rain increases from one month to the next.

What is needed: Which month, compared to the previous one, has more average rain but less average runoff, and this is unique for the year.

Solution:

• Condensed Solution Implementation:
  Examine the rain and runoff values for each pair of consecutive months to see where rain increases but runoff decreases. According to the provided insight, only July fits this pattern.
• Necessary Data points:
  June: Rain = 4.1 in, Runoff = 1.3 in; July: Rain = 4.4 in, Runoff = 1.0 in.
  • Calculations Estimations:
    Rain increases from June to July (\(\mathrm{4.4 \gt 4.1}\)) while runoff decreases (\(\mathrm{1.0 \lt 1.3}\)). This is not true in any other month.
  • Comparison to Answer Choices:
    The choices are Jan, Mar, Jul, and Dec. July is the unique correct answer.

FINAL ANSWER Blank 1: Jul

Question 2: Calculating How Much Rain Exceeds Runoff in That Month

Complete Statement:

when the average amount of rain exceeds the average amount of runoff by approximately ______ inches

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: when
  • Meaning: Refers specifically to the month identified in the first blank (July).
  • Relation to Chart: Focus on July's data only.
• Statement Breakdown 2:
  • Key Phrase: rain exceeds the average amount of runoff
  • Meaning: Subtract the runoff value from the rain value to get the difference.
  • Relation to Chart: Use July's rain and runoff bar heights (rain minus runoff).

What is needed: The numerical difference (in inches) between rain and runoff in July.

Solution:

• Condensed Solution Implementation:
  Subtract July's runoff value from July's rain value, then find the closest match to the answer choices.
• Necessary Data points:
  July's rain: 4.4 in, July's runoff: 1.0 in.
  • Calculations Estimations:
    \(\mathrm{4.4 \text{ in (rain)} - 1.0 \text{ in (runoff)} = 3.4 \text{ in}}\)
  • Comparison to Answer Choices:
    Choices are 1.5, 2.5, 3.5, 4.5. 3.5 is closest to 3.4.

FINAL ANSWER Blank 2: 3.5

Summary

The answer to the first blank is 'Jul' because it's the only month where rain increases and runoff decreases compared to the previous month. The answer to the second blank is '3.5' since the rain exceeds runoff by 3.4 inches in July, making 3.5 (rounded) the best answer.

Question Independence Analysis

The two questions are dependent: the answer to the second is based specifically on the month identified in the first. You must answer the first to meaningfully answer the second.