Question

The dot plots show the salaries for the employees at two small companies before a new company head is hired at each company.3090 100 110 120 13040 50 60 70 80salaries at company 1 in thousands of dollars3040 50 60 70 8090 100 110 120130salaries at company 2 in thousands of dollars7Select all the statements that must be true.A The median values of salaries shown in the dot plots for the two companies are about the same.BThe mean and median values of salaries shown in the dot plot for company 2 are the same.cThe median value of salaries at company 1 will remain unchanged after a company head is hired to have a salary of 500 thousand dollars.DThe standard deviation of salaries shown in the dot plot for company 2ater than the standard deviation of salaries at company 1.The new company head with a salary of 500 thousand dollars will affect the mean value for salaries at company 2 more than the median value for salarieshp

Answer 1

Let's determine whether each statement is true.

Let's start with Statement A. Let's check the median of each dot plot.

For Company 1, we can easily see that the median value is 80 since the dot plot is normally distributed.

For Company 2, the data are skewed so we need to count manually where the median is located. Let's count how many dots are in the dot plot of Company 2.

There are 49 dots in the dot plot of Company 2. The median value would be the center of the data and that is the 25th dot starting from the left.

As we can see in the dot plot, the 25th dot is found at 60. Hence, the median value for Company 2 is 60.

Since the median for Company 1 is 80 and the median for Company 2 is 60, then Statements A and B are not true.

Statement C is true because median values are not easily affected by outliers.