An author is writing a biography of a historical figure. As part of his research, the author tracked all descendants...

Owning The Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

• The diagram uses clear hierarchical rings to trace all living and deceased descendants across three generations, with markers and fractions indicating current survival rates per branch.
• Proportional data (fractions in the outer ring) enable direct calculation of which child has the most living descendants and what percentage of that child's total descendants are alive.
• The largest share of living descendants is associated with one specific child (Child 3 in most chart conventions), and a significant proportion—about \(50\%\)—of all living descendants are from this branch, with a high survival percentage (the best-matching multiple-choice option is about \(80\%\)).
• Visual cues (color, "alive" labels, and fractions) make it easy to spot differences in lineage vitality between branches and identify living family members with and without children.

Step-by-Step Solution

Question 1: Which child has 50% of the living descendants?

Complete Statement:

Fifty percent of the living descendants of the historical figure are descendants of Child ___

Breaking Down the Statement

Statement Breakdown 1:

• Key Phrase: Fifty percent of the living descendants
  • Meaning: Half of all people currently alive who are descendants of the original historical figure.
  • Relation to Chart: We need to add up the number of living descendants for all branches (corresponding to each child) and determine which child's branch equals \(50\%\) of the total.
  • Important Implications: We must sum the living descendants for each child and compare each child's number to the grand total, looking for the branch who contributes half of all living descendants.

Statement Breakdown 2:

• Key Phrase: descendants of Child ___
  • Meaning: The line of all descendants coming from a specific child (Child 1, Child 2, or Child 3).
  • Relation to Chart: The sunburst chart is divided into three colored segments, one per child; all people in a segment are descendants of that child.
  • Important Implications: We examine one colored section at a time and sum its living descendants to compare with the total.

What is needed: Which child (1, 2, or 3) is responsible for exactly \(50\%\) of the currently living descendants.

Solution:

• Condensed Solution Implementation:
  Sum the living descendants for each child, then sum all living descendants, and check which child's total matches \(50\%\) of the overall total.
• Necessary Data points:
  Child 1: living = 7, Child 2: living = 6, Child 3: living = 13; Total living descendants = 26.
  • Calculations Estimations:
    Child 1: \(\frac{7}{26} \approx 27\%\); Child 2: \(\frac{6}{26} \approx 23\%\); Child 3: \(\frac{13}{26} = 50\%\).
  • Comparison to Answer Choices:
    Child 3's branch corresponds to \(50\%\) of all living descendants; it fits the blank.

FINAL ANSWER Blank 1: 3

Question 2: What percentage of that child's descendants are living?

Complete Statement:

...and ___% of that child's descendants are living.

Breaking Down the Statement

Statement Breakdown 1:

• Key Phrase: that child's descendants
  • Meaning: All descendants (living and dead) from the child identified in blank 1, i.e., Child 3.
  • Relation to Chart: We use the summed denominators for Child 3's branch to get total descendants.

Statement Breakdown 2:

• Key Phrase: % ... are living
  • Meaning: What percent of that child's total descendants are alive today.
  • Relation to Chart: Sum the numerators (living) and denominators (total) of the living/total descendant fractions for Child 3, then convert to percent.

What is needed: What percent of Child 3's total descendants are currently alive.

Solution:

• Condensed Solution Implementation:
  Add up the counts of living and total descendants (from fractions) in Child 3's branch. Divide living by total and convert to a percent.
• Necessary Data points:
  Child 3: living = 13 (numerators 2+0+2+4+5), total = 16 (denominators 2+0+3+4+7).
  • Calculations Estimations:
    \(\frac{13}{16} = 0.8125\) or \(81.25\%\).
  • Comparison to Answer Choices:
    \(81.25\%\) rounds to the nearest given choice, \(80\%\).

FINAL ANSWER Blank 2: 80

Summary

Child 3 accounts for 13 out of 26 living descendants (\(50\%\)), and 13 out of 16 total descendants from Child 3 are still alive, which is about \(80\%\). Thus, blanks 1 and 2 are '3' and '80', respectively.

Question Independence Analysis

These questions are sequentially dependent: the second blank refers specifically to 'that child' identified in blank 1. The percentage calculation in blank 2 requires knowing which child was the answer in blank 1.