Question

Using her data set regarding the working conditions and stress levels of domestic workers, Callie has calculated the standard deviation of their housing expenses in two ways, with and without the workers who have zero housing expense. When she includes all workers, the standard deviation is ____.

a.
smaller
c.
the same
b.
larger
d.
scattered

Answer 1

When calculating the standard deviation of a data set, including or excluding certain data points can affect the result. In this case, including or excluding workers with zero housing expense impacts the standard deviation of housing expenses for domestic workers.

Step-by-step explanation:

When calculating the standard deviation of a data set, the inclusion or exclusion of certain data points can affect the result. In this case, Callie has calculated the standard deviation of housing expenses for domestic workers both with and without workers who have zero housing expense.

When she includes all workers, the standard deviation would be larger because the zero expense values would increase the overall variability in the data. On the other hand, if she excludes the workers with zero housing expense, the standard deviation would be smaller because those values are not contributing to the spread of the data.

Therefore, the correct answer is (b) the same.