Multiple Populations and Inferences

Multiple populations When you analyze a group, you usually have a question that you want answered about the group. Use one population when you have a question about a trait of the whole group. How many students in my school play a sport? Use two populations when you want to compare two groups or two parts of a group. Are students who play a sport generally taller than students who do not play a sport? Use the number of populations needed to answer the question you have. How many students play a sport in each grade level?

examples A teacher gave a test to each of her three math classes. To answer each question, should the teacher consider the classes as three populations or as one population? What was the highest score overall? Which is the top-scoring class? What is the mean score in each class? Who is the top-scoring student in each class? What is the mean score of all students? How does the range of scores compare among classes?

examples What was the highest score overall? One population Which is the top-scoring class? Three populations What is the mean score in each class? Three populations Who is the top-scoring student in each class? Three populations What is the mean score of all students? One population How does the range of scores compare among classes? Three populations

examples The school nurse tested the eyesight of all the students in Grades 6, 7, and 8. To answer each question, should the nurse consider the grades as three populations or as one population? How many students have perfect vision in the school? What is the mean eyesight score for each grade? Do students’ eyesight scores change more between 6th and 7th grades, or between 7th and 8th grades?

examples How many students have perfect vision in the school? One population What is the mean eyesight score for each grade? Three populations Do students’ eyesight scores change more between 6th and 7th grades, or between 7th and 8th grades? Three populations

Why can one population in a study be considered more than one population in another study? One study can focus on the entire population. Another study may want to know how different sections of the larger population compare to each other, so the population needs to be considered as more than one population in that case.

examples A researcher is analyzing United States census data. For each question, how many population(s) should the researcher use? Describe the population(s). Do more people live in Maine or in Hawaii? Is the median number of people per residence greater in Chicago, Los Angeles, or Philadelphia? What is the age of the oldest U.S. citizen? What percent of each state’s population is male?

examples Do more people live in Maine or in Hawaii? 2 populations; population of maine and population of hawaii Is the median number of people per residence greater in Chicago, Los Angeles, or Philadelphia? 3 populations; population of Chicago, population of los angeles, population of philadelphia What is the age of the oldest U.S. citizen? 1 population; population of entire united states What percent of each state’s population is male? 50 populations; population of each of the 50 states

examples A scientist is analyzing sea urchin samples taken from the ocean. For each question, how many population(s) should the scientist use? Describe the population(s). How many species of sea urchins exist? Which continent has the greatest population of sea urchins along its coast? Do more sea urchins live in the Atlantic Ocean or in the Pacific Ocean?

examples How many species of sea urchins exist? 1 population; the population of sea urchins in the entire water system on earth Which continent has the greatest population of sea urchins along its coast? 7 populations; the population of sea urchins along the coast of each of the 7 continents: Africa, North America, South America, Asia, Australia, Antarctica, and Europe Do more sea urchins live in the Atlantic Ocean or in the Pacific Ocean? 2 populations; the population of sea urchins in the Atlantic Ocean and the population of sea urchins in the Pacific Ocean

inferences When you make a judgment by interpreting a set of data, you are making an inference.

Comparative inferences  An inference that compares two things is called a comparative inference.

examples The table shows the lengths of a random sample of koi fish from two koi ponds. POND A POND B 2 6 7 10 11 5 8 9 4 12 13 14

examples Make a conjecture about why there are two peaks in the dot plots of both samples. Based on your conjecture, make a comparative inference about the fish in the two ponds.

examples The dot plot shows the lengths of koi fish. The right-most peak represents the adult fish. The left-most peak, showing koi of shorter length, represents the baby fish. In the dot plot for pond b the two peaks are closer together than they are in the dot plot for pond a. So, there is less difference in length between the baby fish and the adult fish in pond b than between the baby fish and the adult fish in pond a.

The table shows the number of hours that a random sample of students in two classes spent on schoolwork last night. CLASS A CLASS B 1 4 5 6 2 3

examples Make a conjecture about why there are two peaks in the dot plot of Class A. Based on your conjecture, make a comparative inference about the students in each class.

examples The students in each class are working in pairs on a project the day before it is due. The two peaks in class A represent the pairs who almost finished the project and the pairs who waited until the last minute to work on the project. The students in class B manage their time better than the students in class A. The students in class B had to spend less time on the project the day before it was due.

Close and check When does a group represent one population? When looking at traits of the group as a whole. When does it represent more than one population? When comparing that trait between different types of members in the group. How can you tell? You can tell how many populations there are by the statistical question you ask.