Question

using the histograms, what is a correct comparison of public and private starting salaries?
both salary distributions are skewed left
in both groups, more than 10 percent of salaries are greater than $55,000
the median salary for both groups is between $45,000 and $50,000
both private and public salaries range from a low of $35,000 to $40,000 to a high of $60,000 to $65,000

Explanation:

Step1: Analyze the skewness

A left - skewed distribution has a longer tail on the left. Looking at the histograms, neither distribution has a long left - tail. So the statement “Both salary distributions are skewed left” is incorrect.

Step2: Check the percentage of salaries greater than $55,000$

For a cumulative relative frequency histogram, if we consider the group for salaries greater than $55,000$ (i.e., the last two bars for each histogram).
Let's assume the cumulative relative frequency at $55$ (in thousands) and subtract the cumulative relative frequency at $50$ (in thousands).
For the left (public) histogram:
Let \(C_{55}\) be the cumulative relative frequency at \(x = 55\) and \(C_{50}\) be the cumulative relative frequency at \(x = 50\).
\(C_{55}-C_{50}>0.1\) (since the height of the bar from \(50 - 55\) and \(55 - 60\) in terms of cumulative relative frequency increase is more than \(10\%\))
For the right (private) histogram:
Let \(C_{55}\) be the cumulative relative frequency at \(x = 55\) and \(C_{50}\) be the cumulative relative frequency at \(x = 50\).
\(C_{55}-C_{50}>0.1\)

Step3: Analyze the median

The median is the value for which the cumulative relative frequency is \(0.5\).
For the left (public) histogram, the cumulative relative frequency reaches \(0.5\) in the \(50 - 55\) (in thousands) range. So the statement “The median salary for both groups is between $45,000$ and $50,000$” is incorrect.

Step4: Analyze the range

The left (public) histogram has a starting point (non - zero cumulative relative frequency) at \(35\) (in thousands), and the right (private) histogram has a starting point (non - zero cumulative relative frequency) at \(30\) (in thousands). So the statement “Both private and public salaries range from a low of $35,000$ to $40,000$ to a high of $60,000$ to $65,000$” is incorrect.

Answer:

In both groups, more than 10 percent of salaries are greater than $55,000$.