The graph shows, for 7 groups—Groups A through G—the relationship between the median and the arithmetic mean of annual salaries...

Owning the Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

• Groups A, C, and G have median salaries higher than their mean salaries; hiring at the median will increase their mean salary.
• Group G, with the largest gap \(109\%\), will see the greatest percentage rise in mean salary after hiring.
• For Groups B, D, E, and F, where the median is below the mean, hiring at the median salary will decrease their mean salary.

Step-by-Step Solution

Question 1: Number of Groups with Mean Increase

Complete Statement:

For exactly _____ of the groups, the addition of the new worker will result in an increase in the arithmetic mean salary for the group.

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: addition of the new worker
  • Meaning: Each group hires a new employee.
  • Relation to Chart: The new worker is paid at the group's median salary.
  • Important Implications: The effect on mean depends on whether the median is greater or less than the mean.
• Statement Breakdown 2:
  • Key Phrase: increase in the arithmetic mean salary
  • Meaning: The group's average salary rises after adding the new worker.
  • Relation to Chart: This increase happens if the median is above the mean \(\mathrm{median/mean} \gt 100\%\).
  • Important Implications: Count groups where median as a percentage of mean is over \(100\%\).
• What is needed: The number of groups whose median salary is above their mean salary \(\mathrm{median/mean} \gt 100\%\).

Solution:

• Condensed Solution Implementation:
  List each group's median-as-percent-of-mean, then count all above \(100\%\).
• Necessary Data points:
  Group A: \(101\%\); Group B: \(94\%\); Group C: \(106\%\); Group D: \(91\%\); Group E: \(96\%\); Group F: \(98\%\); Group G: \(109\%\)
• Calculations Estimations:
  Groups A \((101\%)\), C \((106\%)\), and G \((109\%)\) are all above \(100\%\). That totals 3 groups.
• Comparison to Answer Choices:
  Of the choices provided (2, 3, 4, 5, 6, 7), '3' matches our count.

FINAL ANSWER Blank 1: 3

Question 2: Group with Greatest Percentage Increase

Complete Statement:

For Group _____, the increase (as a percentage of the previous arithmetic mean) will be the greatest.

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: the increase...will be the greatest
  • Meaning: Which group will see the largest increase in its average salary.
  • Relation to Chart: The group with the highest median/mean percentage will get the largest mean boost after hiring at median.
• Statement Breakdown 2:
  • Key Phrase: as a percentage of the previous arithmetic mean
  • Meaning: How big the increase is, relative to the group's original mean.
  • Relation to Chart: A higher median versus mean percentage leads to a greater relative increase.
• What is needed: The group (with median above mean) that has the highest median/mean percentage.

Solution:

• Condensed Solution Implementation:
  From the three groups that increase the mean (A, C, G), select the one with the largest median/mean percentage.
• Necessary Data points:
  A: \(101\%\); C: \(106\%\); G: \(109\%\)
• Calculations Estimations:
  \(\mathrm{G}\,(109\%) \gt \mathrm{C}\,(106\%) \gt \mathrm{A}\,(101\%)\), so Group G sees the largest increase.
• Comparison to Answer Choices:
  Provided choices include 'G', which matches our finding.

FINAL ANSWER Blank 2: G

Summary

Exactly 3 groups (A, C, and G) will see their mean salary increase after hiring a new worker at the median. Among these, Group G will have the greatest percentage increase, due to its median salary being furthest above its mean.

Question Independence Analysis

The questions are dependent: the second uses the set of groups identified as increasing in the first. Both rely on understanding the relationship between median and mean.