5.04 Formulate questions and collect data

What kind of transportation do students at my school use to get to school?

We want to look at if the responses to this question would be be numerical, like a quantity, or not, like a category or word.

Answer to this question could include things like:

• Bike

• Bus

• Car

• Walk

These are categories, not quantities or numbers, so this data is not numerical.

This data could be organized in a pictograph which is used for categorical data, not numerical.

How do the heights of students in your class vary?

We want to know if we can measure or do calculations with the answers to this question.

Height is something that we can measure, so this is numerical data.

If we measure to the nearest quarter inch, it is unlikely that any two students in the class would be the exact same height, so we would need to group this numerical data in order to organize and analyze with it.

If we tried to make a display, like a dot plot or bar graph, without grouping or rounding to the nearest inch, there would be too many values along the horizontal axis.

What is a typical score for a hockey team in a single NHL game?

We need to be able to count or measure the score for it to be numerical.

The score of a hockey game is the number of goals, so it is numerical.

NHL hockey games are generally fairly low scoring with an average of around 3 goals per game and the highest score ever being 14 goals. This data does not need to be grouped as it does not have a very wide spread or possible responses.

For the first game of the 2023-2024 season, this is what a dot plot would look like:

How many years has the Boston Red Sox baseball team been around?

A well formulated question should have a variety of possible answers and relate to a specific population.

There is one answer and no clear population, so this is not a well formulated question for the data cycle.

A related question we could use the data cycle for is "How many years does the average MLB player play for?"

How do the heights of 7th and 8th graders at my school compare?

A well formulated question should have a variety of possible answers and relate to a specific population.

This is a well formulated question as height is a clear attribute with different possible answers.

This data would be numerical and need to be grouped.

What is the distribution of ages at the local martial arts studio?

There is a clear population of people at the local martial arts studio. Now we need to check if data could be collected to give a variety of answers.

Different martial arts athletes will have different ages, so this something we could find data on. This is a well formulated question.

What are the advantages of doing a sample? Select all that apply.

Using a sample requires asking fewer people than if looking at the whole population.

Since a sample requires surveying fewer people, it would usually be cheaper to conduct and it would take less time.

The correct options are A and D.

For option B, our goal is to have the sample represent the population, but we have to be very careful to select a good sample that represents the population. Not all samples are good samples.

What are the disadvantages of doing a sample? Select all that apply.

Use the fact that samples do not survey the whole population being considered.

Because the whole population is not being surveyed, the results of a sample would be less accurate. Also, the sample may not be random or not large enough which would be poor sampling.

The correct options are C and D.

Identify the target population.

The target population will be students at that school. This will impact students since student would get the opportunity to play on the team, but also because money spent adding a soccer team could not be spent adding other opportunities at the school.

This decision could impact other people such as parent, coaches, and school staff, but the target population will be the students that have the opportunity to join the team.

What method would be best to find out how the students feels about the addition of a new sport?

The chosen method should be realistic and ethical to action. It should also give data that is useful for the specific population.

Since we want to find out students' opinions about the addition of soccer, we should use a survey.

Explain why surveying members of the football team about their preference is not representative of the population.

For the sample to be representative of the population, different types of students of varying ages with various hobbies should have an opportunity to express their opinion.

The football team members could be more athletic than other students, or they could not want a new sport to potentially split some of their players.

Finally, there may not be many team members, but the population of the total students at the school might be relatively large in comparison.

Formulate a question to help him complete his investigation.

Donovan needs to choose a particular attribute to explore, like temperature, wind, or precipitation (rain, snow, hail).

Donovan could formulate the question:

"How has the number days below freezing in Richmond, Virginia varied over the last 50 years?"

It might be helpful to know what type of data is collected by weather centers before formulating the question. For example, they usually record amount of precipitation (\operatorname{mm} of rain) per day, but not the length of time it was raining for each day.

Could he use observation, measurement, survey, experiment, or acquire secondary sources? Explain.

He is looking for data on times in the past, likely before he was born. He cannot go back in time and collect the data himself.

Donovan should acquire secondary sources. He can't use observation, measurement, survey, or experiments, because the data from those is typically real-time, not historical (in the past).

For a different question, like, "Do you think winters are the same as 50 years ago, colder, or warmer?" he could use a different method.

Explain how Donovan could collect data that could be used to answer his question from part (a).

He would need to find a reliable secondary source that has the data he is looking for. He may need to reformat or summarize the raw data.

He can submit a request through the National Centers for Environmental Information which is run by the NOAA. He will get an email with a spreadsheet that shows the raw data he selected. From there, he can reformat it to find the total for each year.

For example, here is the raw data in tables:

We could organize and analyze this numerical data with a line graph to see the trend over time.

The longer the time period we look at, the more work it would be to analyze. However, the results would be more reliable and tell a more complete story.

How do the temperature trends in your hometown compare to Donovan's?

We can use NOAA's database, or something similar for other countries, to find data for our location or as close as possible. Usually, airports collect excellent weather data, so we may need to use the closest airport.

For hometowns in the US, we can copy and paste this link into our internet browser:\text{https://www.ncei.noaa.gov/weather-climate-links}

Then ask your teacher for help with finding and summarizing the data you need for your hometown.

Here are some questions you can use to compare Donovan's hometown (Richmond, VA) with yours:

• In what ways are the temperature trends similar?

• In what ways are the temperature trends different?

• What was the coldest year in your hometown compared to Donovan's, which was 1996?

• Does the climate in your hometown vary more or less compared to Donovan's?

Answers will vary based on the hometown.

Sometimes we can find nice data displays showing the data we are interested in. Other times, we need to take raw data and summarize it ourselves. Learning to use some formulas and tools in spreadsheets like "SUM" and "Remove duplicates" can be very helpful.