Curriculum Outcomes
Statistics and Probability (Data Analysis): Collect, display, and analyze data to solve problems. 1. Describe the effect of: • bias • use of language • ethics • cost • time and timing • privacy • cultural sensitivity on the collection of data. [C, CN, R, T] [ICT: F4–3.2, F4–3.3] 2. Select and defend the choice of using either a population or a sample of a population to answer a question. [C, CN, PS, R] 3. Develop and implement a project plan for the collection, display and analysis of data by: • formulating a question for investigation • choosing a data collection method that includes social considerations • selecting a population or a sample • collecting the data • displaying the collected data in an appropriate manner • drawing conclusions to answer the question. [C, PS, R, T, V] [ICT: C1–3.5, C4–3.1, C6–3.1, C6–3.2, C7–3.1, C7–3.2, P1–3.4, P2–3.1] |
Things You Need to Know
- Data is often collected through taking a survey or a questionnaire.
- There can be problems with collecting data if we aren't careful. The data we collect might not be accurate.
- One way data isn't accurate is if we have a flawed survey question.
- Survey questions can be flawed in the following ways:
- Bias: the survey question leans the person taking the survey towards a particular response.
- Ex: Do you prefer gross, sugary, unhealthy soft drinks, or do you prefer delicious and nutritious milk?
- Language: the survey question might be difficult to understand, or misleading.
- Ex: Do you not suppose that the least great Prime Minister in Canadian history isn't the one we don't not have right now?
- Ethics: the survey might refer to or deal with inappropriate or illegal content.
- Ex: Suppose a survey promised to give a free digital copy of a song away without getting the rights from the publisher first.
- Cost: is what the survey is looking for actually worth the effort being put into giving the survey?
- Ex: Suppose a company paid $1 million to conduct a survey by mail to find out whether people think the letter A is better than the letter B.
- Time/Timing: is the time or place of the survey appropriate, or will it alter people's responses?
- Ex: Conducting a survey regarding your favourite type of meat at a vegetarian convention.
- Ex: Conducting an annual survey about the noise level at your school, but this year the survey is given during construction season.
- Privacy: can participants refuse to do the survey/can they remain anonymous?
- Ex: Conducting a survey asking people how much money they make, without being allowed to remain anonymous.
- Cultural Sensitivity: is your survey question inclusive to everyone, or does it ignore people of certain cultures/religions/lifestyles?
- Ex: "Which is your favourite meat: beef, chicken, or pork?"
- This doesn't provide an option for people who don't eat meat.
- Ex: "Which is your favourite meat: beef, chicken, or pork?"
- Bias: the survey question leans the person taking the survey towards a particular response.
- A population is simply all of the people/things that are the target of your survey.
- A sample is just a subgroup of your population that actually takes part in the survey.
- Sometimes, you want to/are able to survey the entire population.
- Ex: If you'd like to survey what everyone in your group wants for lunch, you'll survey the entire population (i.e. the group).
- Usually, we just survey a sample of the population.
- Ex: If you want to find out favourite movie genres in your school, you may only want to ask a sample of people, because if your school is large it would take a long time to sample the school population.
- Types of samples:
- Voluntary Response: participants have the choice of whether or not to participate
- Convenience: participants are chosen because of how easy it was to access them
- Random Samples:
- True Random: participants are chosen completely randomly (usually by names drawn, or computer generated)
- Stratified: population is split into groups, and the same fraction of the group size is surveyed in each group.
- Systematic: every other person/object in the population is surveyed (ex: every 100th light bulb made in a factory is tested)
- Depending on what you're looking for, you're going to use a different type of sample.
- A biased sample is a sample that doesn't reflect the population.
- Usually, biased samples are due to having a sample size that is too small. A good rule of thumb is having a sample of at least 30.
- Measures of Central Tendency:
- mean: add all the data up, and divide by the number of data items
- median: order from least to greatest, find the middle number
- If there are two middle numbers, take the mean of those two middle numbers.
- mode: the number/object that appears most often in the list
Interactive Activities
Sample Problems
Class Notes