The graph shows the numbers of medals won by 7 selected countries in the Summer Olympics that were held in...

Owning the Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

• France had the least year-to-year variation in medal counts (range: 33–40), as shown by its nearly flat line on the chart.
• Russia experienced the steepest medal increase between 1996 and 2000 (+26), marking the sharpest trend during the period; after 2004, their count declined.
• The United States had the highest medal counts every Olympics (92–110), demonstrating consistent leadership among the seven countries.

Step-by-Step Solution

Question 1: Least Variance in Medal Counts

Complete Statement:

The variance in the numbers of medals won is the least for [BLANK].

Breaking Down the Statement

• Statement Breakdown 1:

• Key Phrase: variance in the numbers of medals
  • Meaning: Variance refers to how much the medal counts change across the different Olympic years.
  • Relation to Chart: We should look at the medal counts for each country across the four Olympics and see which one's counts are the most consistent.
  • Important Implications: The answer will be the country whose medal totals stay closest to each other (least ups and downs) over the years.

• Statement Breakdown 2:

• Key Phrase: is the least for
  • Meaning: Asks which single country has the smallest amount of change (least variance).
  • Relation to Chart: We need to compare the spread or range of medal counts for the countries listed.
  • Important Implications: Only the country with the most stable number across all four data points will be the answer.

• What is needed: Among France, Russia, United Kingdom, and United States, which country has the smallest spread or variance in medal counts from 1996 to 2008.

Solution:

• Condensed Solution Implementation:
  Examine the medal counts for each country and calculate the range (difference between highest and lowest), then select the country with the smallest range.
• Necessary Data points:
  France: 37, 38, 33, 40; Russia: 63, 89, 91, 71; United Kingdom: 16, 28, 30, 47; United States: 101, 92, 103, 110.
  • Calculations Estimations:
    France's range is \\(40 - 33 = 7\\); Russia's range is \\(91 - 63 = 28\\); United Kingdom's range is \\(47 - 16 = 31\\); United States' range is \\(110 - 92 = 18\\).
  • Comparison to Answer Choices:
    France has the smallest range (7), much lower than the others, meaning France's medal results were the most consistent.

FINAL ANSWER Blank 1: France

Question 2: Projected 2004 Medal Count Based on 1996-2000 Trend

Complete Statement:

If, for each country, the point representing the medals won in 2004 had been on the line determined by the points representing the medals won in 1996 and 2000, then the country that would have won the greatest number of medals in 2004 is [BLANK].

Breaking Down the Statement

• Statement Breakdown 1:

• Key Phrase: on the line determined by the points representing the medals won in 1996 and 2000
  • Meaning: Extend the straight line from the 1996 value to the 2000 value to predict where 2004 could have been.
  • Relation to Chart: Looking at the direction and steepness of the line segment from 1996 to 2000, we project a value for 2004 by moving the same amount as the difference from 1996 to 2000.

• Statement Breakdown 2:

• Key Phrase: won the greatest number of medals in 2004
  • Meaning: After projecting the 2004 values using the trend, among the given countries, who would show the highest number.
  • Relation to Chart: We need to make this projection for each option and compare the resulting numbers.

• What is needed: Among Australia, China, Russia, and United States, which country would have the highest projected medal count in 2004 following its 1996-2000 trend.

Solution:

• Condensed Solution Implementation:
  Find the increase or decrease from 1996 to 2000 for each country, add this number to the 2000 total to estimate the projected 2004 result, and compare these projections.
• Necessary Data points:
  Australia: 41 (1996), 58 (2000); China: 50 (1996), 60 (2000); Russia: 63 (1996), 89 (2000); United States: 101 (1996), 92 (2000).
  • Calculations Estimations:
    Australia: \\(58 - 41 = 17\\), so projected 2004 = \\(58 + 17 = 75\\). China: \\(60 - 50 = 10\\), so projected 2004 = \\(60 + 10 = 70\\). Russia: \\(89 - 63 = 26\\), so projected 2004 = \\(89 + 26 = 115\\). United States: \\(92 - 101 = -9\\), so projected 2004 = \\(92 - 9 = 83\\).
  • Comparison to Answer Choices:
    Of these, Russia has the highest projected 2004 total (115), greater than United States (83), Australia (75), and China (70).

FINAL ANSWER Blank 2: Russia

Summary

For blank 1, France had the most consistent medal counts (least variance) across all four Olympics. For blank 2, projecting each country's trend from 1996 to 2000 forward, Russia would have had the highest medal count in 2004.

Question Independence Analysis

The two blanks are independent. The first concerns consistency across all data points, while the second involves a projection based on only two data points. The solution to one does not affect or give information about the other.