Question

the histogram shows the starting salaries (rounded to the nearest thousand dollars) for college graduates based on a random sample of recent graduates. determine whether the following statement is true or false according to the graph. more college graduates had starting salaries in the $61,000 - $65,000 range than in the $46,000 - $50,000 range. choose the correct answer below. o a. true, because the sum of the heights of the first two bars in the graph is greater than the sum of the heights of the last two bars. o b. true, because the bar for 61 - 65 is taller than the bar for 46 - 50. o c. false, because the bar for 61 - 65 is shorter than the bar for 46 - 50. o d. false, because the bar for 61 - 65 has the same height as the bar for 46 - 50.

Explanation:

Step1: Analyze Option A

Check if the sum of the heights of the first two bars (41 - 45 and 46 - 50) is greater than the bar for 61 - 65.
From the graph, assume the height of 41 - 45 is \(h_1\), 46 - 50 is \(h_2\), and 61 - 65 is \(h_3\). By visual inspection (or if we consider approximate values from the histogram's y - axis), \(h_1+h_2>h_3\).

Step2: Analyze Option B

Check if the bar for 61 - 65 is taller than the bar for 46 - 50.
Since \(h_3 < h_2\) (from the graph's visual comparison of bar heights), this option is false.

Step3: Analyze Option C

Check if the bar for 61 - 65 is shorter than the bar for 46 - 50.
Since \(h_3 < h_2\) (from the graph's visual comparison of bar heights), this option is false.

Step4: Analyze Option D

Check if the bar for 61 - 65 has the same height as the bar for 46 - 50.
Since \(h_3
eq h_2\) (from the graph's visual comparison of bar heights), this option is false.

Answer:

A. True, because the sum of the heights of the first two bars in the graph is greater than the sum of the heights of the last two bars.