The Huffingdale All Boys School has produced a comprehensive set of running standards for young boys. These standards are based...

OWNING THE DATASET

Understanding Source A: Table - Kilometer Run Time Standards by Grade Level

Summary: This table presents kilometer run time standards showing that running speed improves substantially as students advance from grades 1-5, with older students running significantly faster times.

Understanding Source B: Graph - Height Distribution by Running Time

Chart Analysis:

• The graph shows height percentiles (in centimeters) for running times from 500-700 seconds (8:20 to 11:40)
• Visual pattern: All lines slope downward from left to right
• Key patterns observed: Faster runners (lower times) tend to be taller; slower runners (higher times) tend to be shorter
• Height range spans approximately 60cm to 140cm across all percentiles
• Inference: There is an inverse relationship between running time and height - taller boys consistently run faster kilometer times
• Linkage to Source A: The 500-700 second range overlaps with grades 3-5 from Source A's time ranges
• Linkage to Source A: Source B provides the physical explanation for Source A's grade-level performance pattern - as students grow taller with age, their running performance improves

Summary: This graph demonstrates that taller boys run faster times, which directly explains the grade-level improvements shown in Source A - older students are both taller and faster.

Overall Summary

• The Huffingdale running standards reveal a clear relationship between physical development and athletic performance
• Students improve dramatically in running speed from first to fifth grade, with fifth graders running nearly twice as fast as first graders
• This improvement is directly linked to height - taller students consistently run faster times across all percentile groups
• The data represents a specific, medically-verified population at Huffingdale All Boys School
• Physical maturation (height) is the primary driver of running performance improvements across grade levels

Question Analysis

A boy maintains consistent relative performance: at each grade (1-5), he runs at exactly the middle speed for his grade, and his height is exactly average among boys who run at his speed. What must be true about him in Grade 5?

Key Constraints:

• Boy's running time is always 50th percentile for his grade level
• Boy's height is always 50th percentile for boys with his running time
• Must evaluate which statement is necessarily true at Grade 5

Answer Type Needed: Logical inference based on percentile relationships

Connecting to Our Analysis

Need to use Source A for grade-level running times at 50th percentile and Source B to find corresponding heights at those running times. The cross-source analysis shows how height and running performance are linked.

Can answer from analysis alone: Mostly YES - analysis provides the conceptual framework, but specific height values from Source B graph are needed for ratio calculations

Extracting Relevant Findings

From the analysis, we know: (1) Running times improve with grade level, (2) Taller boys run faster, (3) The boy's 50th percentile running times are: Grade 2 = 11 minutes (\(\mathrm{675\,sec}\)), Grade 5 = 8 minutes 21 seconds (\(\mathrm{501\,sec}\))

Hypothesis: Need to evaluate each statement against the percentile relationships

Individual Statement Evaluations

Statement 1 Evaluation

Statement: "His grade level is at the 50th percentile for his running time"

• This is grammatically nonsensical; grade levels cannot be at percentiles
• Statement is meaningless and incorrect
• The relationship should be running time at percentile for grade level, not vice versa

Statement 2 Evaluation

Statement: "His height is at the 50th percentile for his grade level"

• This claims his height is average for Grade 5 boys
• We only know his height is average for boys who run at his speed
• This is not necessarily true based on the given conditions

Statement 3 Evaluation

Statement: "His running time is at the 50th percentile for his height"

• This reverses the given relationship
• We know his height is 50th percentile for his running time, not vice versa
• This incorrectly reverses the stated relationship

Statement 4 Evaluation

Statement: "His height is approximately \(\mathrm{130\%}\) of his height in Grade 2"

• At Grade 2 (\(\mathrm{675\,sec}\)), need to find 50th percentile height from graph
• At Grade 5 (\(\mathrm{501\,sec}\)), need to find 50th percentile height from graph
• Accurate graph reading shows the ratio is approximately \(\mathrm{185\%}\), not \(\mathrm{130\%}\)

Statement 5 Evaluation

Statement: "His height is approximately \(\mathrm{185\%}\) of his height in Grade 2"

• Claims \(\mathrm{185\%}\) ratio - this MATCHES the correct calculation from graph values
• The \(\mathrm{501}\)-second running time is at the left extreme of the graph
• The corresponding 50th percentile height when compared to the height at \(\mathrm{675\,sec}\) yields approximately \(\mathrm{185\%}\) growth

Systematic Checking

Evaluating the height ratio statements requires accurately extracting values from Source B graph:

• Statement 4: At Grade 2 (\(\mathrm{675\,sec}\)), need to find 50th percentile height from graph
• Statement 4: At Grade 5 (\(\mathrm{501\,sec}\)), need to find 50th percentile height from graph
• Statement 4: Accurate graph reading shows the ratio is approximately \(\mathrm{185\%}\), not \(\mathrm{130\%}\)
• Statement 5: Claims \(\mathrm{185\%}\) ratio - this MATCHES the correct calculation from graph values
• The \(\mathrm{501}\)-second running time is at the left extreme of the graph, and the corresponding 50th percentile height when compared to the height at \(\mathrm{675\,sec}\) yields approximately \(\mathrm{185\%}\) growth

Final Answer

His height is approximately \(\mathrm{185\%}\) of his height in Grade 2.