Question

The dot plots show the salaries for the employees at two small companies before a new company head is hired at each company. Which statements about the data sets must be true?

a) Both data sets have the same mean.
b) The data sets have the same range.
c) The median salary increased at both companies.
d) The new company head affected the data sets differently.

Answer 1

The statements that must be true about the data sets are that both data sets have the same mean, the median salary increased at both companies, and the new company head affected the data sets differently.

Step-by-step explanation:

The statements about the data sets that must be true are:

• a) Both data sets have the same mean. Since the mean is the average of all the salaries, it is possible for the two data sets to have the same mean.
• c) The median salary increased at both companies. The median is the middle value in a sorted data set. If the new company head increased the salaries of all employees, the median salary would increase.
• d) The new company head affected the data sets differently. This statement is true because the dot plots show different distributions of salaries for the two companies, indicating that the new company head had a different impact on each data set.