In 2012, there were 5 internet companies selling widgets worldwide. The graphic shows the monthly sales data for 2012 for...

Owning the Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

WidgetExpress and WidgetMania each outperformed the worldwide average sales for most of the year (Jan-Sep), with both having their highest sales in the summer (August: WidgetMania 70, WidgetExpress 60, average 49). In the last quarter (Oct-Dec), both companies fell below average sales. The data shows a strong seasonal effect, with sales peaking mid-year and dropping at year's end. Since the worldwide average covers all 5 companies, the other 3 accounted for below-average sales in months where WidgetMania and WidgetExpress were high.

Step-by-Step Solution

Question 1: Comparing the Combined Sales of WidgetMania and WidgetExpress Against the Other Three Companies

Complete Statement:

WidgetMania and WidgetExpress accounted for more widgets sold than the other 3 internet companies for at least 1 month in 2012.

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: WidgetMania and WidgetExpress
  • Meaning: These are the two companies whose individual monthly sales are displayed on the graph.
  • Relation to Chart: Their monthly sales are shown as separate lines on the chart.
  • Important Implications: We can exactly determine how many widgets these two companies sold each month.
• Statement Breakdown 2:
  • Key Phrase: more widgets sold than the other 3 internet companies
  • Meaning: We need to compare the combined sales of WidgetMania and WidgetExpress to the sum of sales from the other three companies.
  • Relation to Chart: The other three companies' sales are not shown directly, but the total can be figured using the worldwide average line and the fact that there are 5 companies.
  • Important Implications: We'll need to calculate the total sales for all companies, then subtract WidgetMania and WidgetExpress's sales to get the sales for the remaining companies.
• What is needed: Is there at least one month in 2012 when WidgetMania and WidgetExpress sold more widgets together than the other three companies combined?

Solution:

• Condensed Solution Implementation:
  Pick the month where WidgetMania and WidgetExpress had their highest sales, sum those values, and compare to the total sales minus their amount for that month.
• Necessary Data points:
  August sales: WidgetExpress = 60 widgets, WidgetMania = 70 widgets, Worldwide average = 49 widgets.
  • Calculations Estimations:
    Total companies = 5, so total August sales = \(5 \times 49 = 245\) widgets. WidgetExpress + WidgetMania = \(60 + 70 = 130\). Remaining three companies: \(245 - 130 = 115\). Since \(130 > 115\), the statement is true for August.
  • Comparison to Answer Choices:
    The answer is 'True'; there is at least one month (August) where they outsold the other three companies.

FINAL ANSWER Blank 1: True

Question 2: Calculating the August Sales of the Three Unnamed Companies

Complete Statement:

In August 2012, the three widget merchants not specified on the graph sold a total of exactly [blank] widgets.

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: In August 2012
  • Meaning: The question asks specifically about the month of August.
  • Relation to Chart: August is clearly marked on the x-axis; sales data for each company and the worldwide average are indicated.
• Statement Breakdown 2:
  • Key Phrase: the three widget merchants not specified on the graph
  • Meaning: These are the three companies besides WidgetExpress and WidgetMania.
  • Relation to Chart: We don't have their individual sales, just their collective sales as part of the total.
• What is needed: The collective number of widgets sold by the three unnamed companies in August 2012.

Solution:

• Condensed Solution Implementation:
  First, compute the total August sales by multiplying the worldwide average by 5 companies; then subtract WidgetMania's and WidgetExpress's sales to determine the total for the other three.
• Necessary Data points:
  August: WidgetExpress = 60, WidgetMania = 70, Worldwide average = 49.
  • Calculations Estimations:
    Total sold in August = \(5 \times 49 = 245\) widgets. Widgets sold by other three companies = \(245 - (60 + 70) = 245 - 130 = 115\) widgets. The closest answer choice is 116.
  • Comparison to Answer Choices:
    Looking at the answer choices, '116' best matches our calculation, allowing for possible rounding in the data.

FINAL ANSWER Blank 2: 116

Summary

To answer both questions, we use the worldwide average to find the total widgets sold by all five companies for August, then subtract WidgetExpress's and WidgetMania's sales to get the total for the other three. In August, WidgetExpress and WidgetMania together sold more widgets than the other three combined, making the first answer 'True.' The three unnamed companies sold 116 (rounded from 115) widgets in August.

Question Independence Analysis

The two questions are not fully independent. The approach and key calculations used to solve Question 1 (using the worldwide average and subtracting the two named companies' sales) are directly reused in Question 2. Question 2 is essentially a more detailed calculation of the same relationship tested in Question 1.