Statistical variable
What is the favorite band at your school? How many hours a day do kids your age use their cell phones? To answer, you don't need to ask everyone, but you do have to do it well. Statistics starts by deciding who we ask and what we measure.
Population, sample, and individual
Why not always study the whole population? Because it can be very expensive, slow, or even impossible (to check how long light bulbs last you have to burn them out: you can't test them all). When the whole population is studied, it is called a census.
A group of researchers wants to find out the favorite music group of Mexican teenagers aged between 12 and 16. To do this, they conduct a survey among 500 students from…
A group of researchers wants to find out the favorite music group of Mexican teenagers aged between 12 and 16. To do this, they conduct a survey among 500 students from several secundarias in Mexico City. State:
- a) The population under study.
- b) The chosen sample.
- c) The individual.
Imagine that you want to conduct a study on the amount of money young people in your neighbourhood spend weekly on leisure. a) What type of variable is "money spent"? b)…
Imagine that you want to conduct a study on the amount of money young people in your neighbourhood spend weekly on leisure.
- a) What type of variable is "money spent"?
- b) If $1,200$ young people live in the neighbourhood and you ask $60$, what is the sample size?
- c) Would it be representative if you only ask young people standing outside a cinema on a Saturday afternoon? Reason your answer.
To find out citizens' opinions on the construction of a new bike lane in the city center, a local newspaper carries out a survey at the entrance of a shop specializing…
To find out citizens' opinions on the construction of a new bike lane in the city center, a local newspaper carries out a survey at the entrance of a shop specializing in mountain biking.
- a) Do you think the chosen sample is representative of the city's population? Reason your answer.
- b) Is there any type of bias in this choice? Explain why.
- c) Propose a sampling method that would be more suitable to obtain reliable results.
Designing a study: how long does it take us to get to school?
We want to find out the usual one-way travel time of the 48 students in two groups of 24 (3° A and 3° B). Before asking, we agree on what we measure: minutes from leaving home until entering the school on a typical school day, including waiting time. A question like "Does it take you too long?" collects an opinion, not the time.
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We randomly draw 4 students from each group: a sample of 8 with the same proportions as the population. We don't pick only friends or only those who arrive earliest.
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We record group and minutes without names. If someone doesn't respond, we note the absence; we don't make up their time. We agree in advance on how to repeat the draw among the students who still need to be selected.
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We check units, impossible answers, and what each person understands by "usual." We don't discard a high time just because it looks strange: we check it first.
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We organize the data, calculate measures, and write up what we can conclude and what we can't. The sample is small and doesn't automatically represent other grades or other schools.
In the technology section we will work with a fictional sample of 8 times to practice the analysis. In a real study we would also keep the information needed to review how each group was selected.
Types of variables
The statistical variable is the characteristic we study. There are two main types:
| Type | Values | Examples |
|---|---|---|
| Qualitative | Qualities, not numbers | Favorite sport, eye color, social network |
| Discrete quantitative | Numbers that are counted (isolated values) | Number of siblings, pets, goals |
| Continuous quantitative | Numbers that are measured (any value in an interval) | Height, weight, time, temperature |
Classify the following statistical variables as qualitative or quantitative: a) The favorite color of a cell phone case. b) The number of followers on a TikTok account.…
Classify the following statistical variables as qualitative or quantitative:
- a) The favorite color of a cell phone case.
- b) The number of followers on a TikTok account.
- c) The time, in minutes, it takes you to get from home to school.
- d) The brand of sneakers preferred by the students in your class.
Within quantitative variables, we must distinguish between discrete and continuous. State the type of each of the following: a) The number of cousins each student has.…
Within quantitative variables, we must distinguish between discrete and continuous. State the type of each of the following:
- a) The number of cousins each student has.
- b) The capacity, in liters, of the water bottles sold in the cafeteria.
- c) The number of WhatsApp messages you receive in a day.
- d) The weight of the backpacks of 9th grade (3° de secundaria) students.
For each of the following survey questions, identify whether the response would result in a nominal qualitative, discrete quantitative or continuous quantitative…
For each of the following survey questions, identify whether the response would result in a nominal qualitative, discrete quantitative or continuous quantitative variable:
- a) "Which social media application do you use most frequently?"
- b) "How many hours a day (with decimals) do you spend studying?"
- c) "How many times have you been to the cinema in the last month?"
- d) "Which is your preferred operating system (Android or iOS)?"
The following table shows several variables collected in a survey carried out at an e-sports club. Classify each of them as qualitative, quantitative discrete or…
The following table shows several variables collected in a survey carried out at an e-sports club. Classify each of them as qualitative, quantitative discrete or quantitative continuous:
| Variable | Type of variable |
|---|---|
| Favorite video game | |
| Weekly training hours | |
| Number of peripherals (keyboard, mouse...) owned | |
| Brand of monitor used | |
| Internet connection speed (Mbps) | |
| World ranking position |