Population, census and sample surveys. Stats

Population, census and sample surveys. Stats slides.

1. Get ready! For this lesson, you’ll need

2. Number Talk  

3. Representing Data – Project Session Learning intention To be able to represent data Success criteria I can collect my sample data I can choose an appropriate graphical display for my dataset I can create graphical displays for my data set I can draw conclusions from a graphical display I can make predictions using a graphical display

4. Accessing prior knowledge Ms Grant collected data about the favourite fruits of her 100 students. What would be an appropriate graphical display for this data? Learning intention To be able to represent data Success criteria I can collect my sample data I can choose an appropriate graphical display for my dataset I can create graphical displays for my data set I can draw conclusions from a graphical display I can make predictions using a graphical display

5. Project question - Options Discrete How many humans live in your house? How many siblings do you have? How many different countries have you been to? How many pets do you have? How many books have you read this year? How many languages can you speak? How many times do you exercise per week? How many commendations have you received in 2023? How many electronic devices do you own? Continuous How tall are you in centimetres? How many hours do you spend on your phone per day? What is your shoe size? Choose a topic that sounds interesting to you that you will investigate for your project.

6. What are populations and samples? Recall back to our first lesson: Learning intention To be able to represent data Success criteria I can collect my sample data I can choose an appropriate graphical display for my dataset I can create graphical displays for my data set I can draw conclusions from a graphical display I can make predictions using a graphical display A  population  is the entire group that you want to draw conclusions about. A  sample  is the specific group that you will collect data from. The size of the sample is always less than the total size of the population.

7. How can we collect sample data? When collecting sample data it is important that we collect random, unbiased samples. To do this, we need to ensure that every element in a population has an equal chance of being chosen for the sample. What are some ways we can ensure our samples are random? Learning intention To be able to represent data Success criteria I can collect my sample data I can choose an appropriate graphical display for my dataset I can create graphical displays for my data set I can draw conclusions from a graphical display I can make predictions using a graphical display

8. How can we collect sample data? We can also collect stratified random samples. This starts off by dividing a population into groups with similar attributes. Then a random sample is taken from each group. Learning intention To be able to represent data Success criteria I can collect my sample data I can choose an appropriate graphical display for my dataset I can create graphical displays for my data set I can draw conclusions from a graphical display I can make predictions using a graphical display What would be the benefit of generating random samples in this manner?

9. How can we collect sample data? Once you have picked your data, you need to assign each respondent an “ID” Learning intention To be able to represent data Success criteria I can collect my sample data I can choose an appropriate graphical display for my dataset I can create graphical displays for my data set I can draw conclusions from a graphical display I can make predictions using a graphical display

10. How can we collect sample data? To collect random samples, we can use random number generators. Learning intention To be able to represent data Success criteria I can collect my sample data I can choose an appropriate graphical display for my dataset I can create graphical displays for my data set I can draw conclusions from a graphical display I can make predictions using a graphical display You need to generate a sample size of 20. The maximum value of the integers is determined by the number of people who participated in the survey.

11. How can we collect sample data? Learning intention To be able to represent data Success criteria I can collect my sample data I can choose an appropriate graphical display for my dataset I can create graphical displays for my data set I can draw conclusions from a graphical display I can make predictions using a graphical display When you get your 20 numbers , you need to find the corresponding respondents in your data The sample data is:   Note that in this PowerPoint only 10 numbers were chosen, you need to choose 20.

12. How do we determine which graphs are appropriate? Not all graph types are suitable for our data sets. For example, this sample has a small range so we cannot use a stem and leaf plot or histogram. What do you think an appropriate graph type for this data is?   Learning intention To be able to represent data Success criteria I can collect my sample data I can choose an appropriate graphical display for my dataset I can create graphical displays for my data set I can draw conclusions from a graphical display I can make predictions using a graphical display   Number of electronic devices Frequency 1 2 2 3 5 4 2 5 1 Frequency tables can help us to determine the best graph type.

13. How do we determine which graphs are appropriate? As the range is small and it is discrete data, we can use: Bar chart/column graph Dot plot Learning intention To be able to represent data Success criteria I can collect my sample data I can choose an appropriate graphical display for my dataset I can create graphical displays for my data set I can draw conclusions from a graphical display I can make predictions using a graphical display Number of electronic devices Frequency 1 2 2 3 5 4 2 5 1 Number of electronic devices 3 1 5 2 4 Number of electronic devices owned by Year 8 Students at VUSC (sample size 10)

14. How do we construct comparison graphs? Learning intention To be able to represent data Success criteria I can collect my sample data I can choose an appropriate graphical display for my dataset I can create graphical displays for my data set I can draw conclusions from a graphical display I can make predictions using a graphical display First, generate a comparison frequency table Number of electronic devices Frequency (Sample A) Frequency (Sample B) 1 1 2 2 4 3 4 3 4 2 5 1 2 Choose an appropriate graph type. Make sure to label the axes and show the different samples clearly!

15. Check for understanding Why is it important that we choose random samples when collecting data? How can we best try to ensure we collect random samples? Learning intention To be able to represent data Success criteria I can collect my sample data I can choose an appropriate graphical display for my dataset I can create graphical displays for my data set I can draw conclusions from a graphical display I can make predictions using a graphical display

16. Apply understanding - Project For your chosen question, you need to: Assign respondent IDs to each participant Generate 20 random numbers to generate your random sample. This is Sample A. Generate another 20 random numbers to generate your other random sample. This is Sample B. Depending on the range of the data (highest value – lowest value) Develop frequency tables for each sample (this may need to use class intervals depending on data determine two appropriate graph types for the data and represent both samples using both types (4 graphs) Develop a comparison graph ( eg side by side bar chart, back to back stem and leaf plot. Learning intention To be able to represent data Success criteria I can collect my sample data I can choose an appropriate graphical display for my dataset I can create graphical displays for my data set I can draw conclusions from a graphical display I can make predictions using a graphical display

17. Review learning intention Name one type of graph that would not have been appropriate for your data set and explain why this is the case. Learning intention To be able to represent data Success criteria I can collect my sample data I can choose an appropriate graphical display for my dataset I can create graphical displays for my data set I can draw conclusions from a graphical display I can make predictions using a graphical display

18. Post and Effort Rating Use the success criteria to give yourself a post rating and effort rating for this topic. Learning intention To be able to represent data Success criteria I can collect my sample data I can choose an appropriate graphical display for my dataset I can create graphical displays for my data set I can draw conclusions from a graphical display I can make predictions using a graphical display

19. Summary and Review (At home) In your summary section of your notes: Key point 1 Key point 2 Key point 3 Learning intention To be able to represent data Success criteria I can collect my sample data I can choose an appropriate graphical display for my dataset I can create graphical displays for my data set I can draw conclusions from a graphical display I can make predictions using a graphical display

20. Action icons Turn and talk as a pair Think on your own Talk as a table group Dot point your notes Write down what your group spoke about Write in full sentences Draw a picture to represent Be ready to be called on to share Listen to instructions Stop and look Watch me demonstrate Read on your own Do this part silently Exit pass Brainstorm Draw this table Use your calculator