The graph shows, for the first five weeks in each of three years, the number of visitors to websites devoted...

Owning The Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

The data shows a clear year-on-year increase in real estate website visitors in New Zealand for the first five weeks of each year, with 2007 having the lowest traffic and 2009 the highest. The maximum value occurs in week 5, 2009 (850,000), while the minimum is in week 3, 2007 (650,000), giving a range of 200,000. The chart's grouped bars allow straightforward visual comparison and make the growth trend and outlier points easy to identify.

Step-by-Step Solution

Question 1: Finding the Range Among 15 Weeks

Complete Statement:

For the 15 weeks shown, the range of numbers of visitors is equal to the number for ______

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: For the 15 weeks shown
    • Meaning: Consider all weeks from all three years, forming a set of 15 data points.
    • Relation to Chart: Every vertical bar in the chart, regardless of year, is counted.
    • Important Implications: Do not calculate range year by year; use all displayed data.

• Statement Breakdown 2:
  • Key Phrase: range of numbers of visitors
    • Meaning: The mathematical range is the difference between the largest and smallest value in the data set.
    • Relation to Chart: Need to find the tallest and shortest bars across all 15.
    • Important Implications: \(\mathrm{Range} = \mathrm{maximum} - \mathrm{minimum}\).

• What is needed: Which week-to-week difference equals the overall range for all 15 weeks.

Solution:

• Condensed Solution Implementation:
  Find the highest and lowest visitor numbers among all weeks, calculate their difference, and confirm which answer choice matches that difference.
• Necessary Data points:
  Max: Week 5, 2009 (850,000); Min: Week 3, 2007 (650,000).
  • Calculations Estimations:
    \(\mathrm{Range} = 850,000 - 650,000 = 200,000\).
  • Comparison to Answer Choices:
    The answer that matches 200,000 is 'Week 5, 2009, minus that for Week 3, 2007.'

FINAL ANSWER Blank 1: Week 5, 2009, minus that for Week 3, 2007

Question 2: Comparing the Range and the Median

Complete Statement:

For the 15 weeks shown, the range of numbers of visitors is ______ the median of the numbers of visitors.

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: range of numbers of visitors
    • Meaning: Refers to the just-calculated difference between the largest and smallest values.
    • Relation to Chart: 200,000 as already determined.

• Statement Breakdown 2:
  • Key Phrase: the median
    • Meaning: The middle value when all 15 weekly numbers are sorted.
    • Relation to Chart: With 15 numbers, median is the 8th in ascending order.

• What is needed: The relationship (less than, equal to, or greater than) between the range and the median.

Solution:

• Condensed Solution Implementation:
  Sort all visitor numbers, find the eighth value for median, then compare range (200,000) to median.
• Necessary Data points:
  Sorted visitor numbers: 650,000; 670,000; 700,000; 710,000; 725,000; 770,000; 770,000; 800,000; 810,000; 810,000; 825,000; 825,000; 830,000; 840,000; 850,000. Median = 800,000.
  • Calculations Estimations:
    \(\mathrm{Range\ (200,000)} \lt \mathrm{Median\ (800,000)}\).
  • Comparison to Answer Choices:
    "Less than" accurately describes this relationship.

FINAL ANSWER Blank 2: Less than

Summary

To answer these questions, we combined all 15 bars across years as one data set. The range is 200,000 (850,000 minus 650,000), specifically the difference between Week 5, 2009 and Week 3, 2007. The range (200,000) is less than the median value (800,000) once all the values are sorted.

Question Independence Analysis

The two questions are connected because both require considering all 15 data points together and not by single year. Question 2 relies on the result from Question 1, since both reference the same computed range. Therefore, the answers are not fully independent.