# Math Inferences Worksheets

The ultimate goal for anyone learning math is to use it to make better and more confident decisions. The goal is to be able to make inferences from any given data sets. This is not something that you can teach or learn in a single class. Learning to make inferences requires a good deal of experience and a consistent method of reflection. You should not only be concerned that you are getting the correct answer, but that you used all of the different means that were available to you to make sense of what ever data you were analyzing. This selection of worksheets and lessons will help you learn to make well thought out decisions based on data that is collected.

### Aligned Standard: Grade 7 Statistics - 7.G.SP.A.2

- Ape Population Step-by-step Lesson- This is why they tag animals in the wild.
- Guided Lesson - We go from alligators to cafeteria menus to tracking chips in this one.
- Guided Lesson Explanation - This is a really good skill to work on. I find it useful for students.
- Practice Worksheet - This one took a long time to write. It will also take a long time to complete.
- Matching Worksheet - Match the problems to the numbers present.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Students that see this for the first time always say things like, "That is how National Geographic does it!"

- Homework 1 - Troy has to complete a research project on the African Elephant population in Africa. He is trying to estimate the size and population of African Elephants. He randomly catches 25 African Elephants and tags them. He releases the elephants into the jungle. A few days later, he observed 100 African Elephants, 15 of which were tagged.
- Homework 2 - The School Health Department wants to open a cafeteria in the school. So they collected data from two random samples of 100 students regarding student s lunch preference? Make at least two inferences based on the results.
- Homework 3 - A hardware company wants to test their hardware. They tagged 25 pieces. The following year, 150 pieces are returned and found that 18 were tagged. What is the best estimation of the hardware sales?

### Practice Worksheets

Time to focus on data that is already collected.

- Practice 1 - The animal department wants to estimate the kangaroo population. So they marked 30 kangaroos with paint. These kangaroos were then released into the jungle. After four months 600 kangaroos were caught. Among these Kangaroo, 18 were marked. To the nearest whole number, what is the best estimate for the kangaroo population?
- Practice 2 - Sara collected two random samples of 100 children regarding their favorite cartoon. Make at least two inferences based on the results.
- Practice 3 - The government of Russia declared Siberian Tiger as an endangered animal. They tied a belt around the legs of 20 Siberian Tigers and released them. A year later, they found 160 Siberian Tigers; among those Siberian Tigers, 16 had belts. Find the best estimate for the population?

### Math Skill Quizzes

Very wordy problems result in less problems per page.

- Quiz 1 - Edward was given a project to research the leopard population in Spain. He randomly catches 44 leopards and marks them with paint. He releases the leopards in the jungle. The following year he observes 220 leopards and he found that 11 were marked with the paint that he used. Find out the best estimate for the size of the leopard population?
- Quiz 2 - Gerald collected two random samples of 100 women regarding their favorite color of folder. Make an inference from the data.
- Quiz 3 - A famous television channel put tags on 48 butterflies and released them. Later, they catch 450 butterflies; among those 24 were tagged. Calculate the best estimate for the butterfly population?

### How Do You Make Inferences from Random Data?

There will be many times in your life where you are looking at what can seem like an endless stream of data, and you have been tasked with making sense of it all. This can overwhelm you at first, but you just need to ask yourself what is sticking out at you about each data set that you analyze. There is always something, you just have to find it.

Students start developing inferences from random data throughout the 7th and 8th grade standard. It is one of the things that students should learn. Students are often given random data for making population inferences. Any random data is a subset of the population. Random samples are more likely to contain data that can later be used for making probable predictions for the entire population. The size of the population determines the strength of the inference. For example, the larger the sample size, the stronger will be the inference. The more data you have the more reliable the data. This is because there is more proof available that the trends that exist are consistent.

For example, a home builder surveyed 50 customers to find out how (i.e., through which medium) people have heard about their business.

Solution: If the circle incorporates the entire population of 110,000 people and the builder should only need to choose one type of marketing for the next year, which option should he choose and why?

Based on this random sampling, the strength of the inference can be weak because there are only 50 customers out of the entire population size where the city was surveyed. When you think about it 50 out of 110,000 people represents less then 5 hundredths percent (50/110,000) of the population.

Based on this quantitative description, it is most likely that the builder will choose "friend referral" because half the surveyed customers found out about the builder from the friends.