Statistical concepts
A town council wants to find out how many young people use the cycle lane. It cannot ask everyone, so it chooses a few people and, from their answers, draws conclusions about everybody. For those conclusions to be worth anything, you have to choose well who to ask and what to record: that is the first thing statistics teaches.
Population, sample and individual
To find out the favourite video game of the students at a secondary school of $850$ students, a survey was given to $40$ students chosen at random during break. Identify…
To find out the favourite video game of the students at a secondary school of $850$ students, a survey was given to $40$ students chosen at random during break. Identify the following elements of the study:
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Population
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Sample
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Individual
A study is to be carried out to find out the favourite ice cream flavour of the inhabitants of a town of $50.000$ people. To do this, the first $100$ customers entering…
A study is to be carried out to find out the favourite ice cream flavour of the inhabitants of a town of $50.000$ people. To do this, the first $100$ customers entering a town centre ice cream shop on a Monday morning are asked.
Do you think this sample is representative of the entire population of the town? Briefly explain your answer.
A city council wants to know the digital leisure habits of teenagers aged between 12 and 16. To do this, it randomly selects 400 students from three different secondary…
A city council wants to know the digital leisure habits of teenagers aged between 12 and 16. To do this, it randomly selects 400 students from three different secondary schools and asks them how many hours per day on average they spend on social media (TikTok, Instagram, etc.).
Identify the following elements of the statistical study:
- a) The population.
- b) The sample.
- c) The individual.
- d) The statistical characteristic studied and its classification.
Qualitative variables: nominal and ordinal
The statistical variable is what is measured for each individual. Qualitative variables take values that are not numbers but qualities.
Classify the following statistical variables as qualitative or quantitative: a) Your friends' favourite colour. b) The number of WhatsApp messages you receive per day.…
Classify the following statistical variables as qualitative or quantitative:
- a) Your friends' favourite colour.
- b) The number of WhatsApp messages you receive per day.
- c) The brand of trainers worn by the students in your class.
- d) The amount of money you save each month.
Look at the following statistical variables related to a school trip and classify them: 1. Destination country. 2. Duration in number of days. 3. Distance travelled in…
Look at the following statistical variables related to a school trip and classify them:
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Destination country.
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Duration in number of days.
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Distance travelled in kilometres.
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Level of satisfaction (Very low, Low, Medium, High).
Quantitative variables: discrete and continuous
| Type | Values | Examples |
|---|---|---|
| Nominal qualitative | Qualities with no order | Phone brand, film genre |
| Ordinal qualitative | Qualities with an order | Star rating, satisfaction |
| Discrete quantitative | Numbers that are counted | No. of messages, of siblings, of goals |
| Continuous quantitative | Numbers that are measured | Usage time, temperature, distance |
Classify these quantitative variables as discrete or continuous: a) The number of cousins each student has. b) The exact time it takes you to get from home to school. c)…
Classify these quantitative variables as discrete or continuous:
- a) The number of cousins each student has.
- b) The exact time it takes you to get from home to school.
- c) The temperature of a drink can when coming out of the vending machine.
- d) The number of books in your classroom library.
An animal shelter has recorded the age (in years) of the dogs adopted over the last month. The data obtained is as follows: $$2, 1, 5, 3, 2, 4, 1, 2, 3, 2, 5, 1, 4, 2,…
An animal shelter has recorded the age (in years) of the dogs adopted over the last month. The data obtained is as follows:
$$2, 1, 5, 3, 2, 4, 1, 2, 3, 2, 5, 1, 4, 2, 3$$Construct a frequency table that includes:
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Variable ($x_i$)
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Absolute frequency ($n_i$)
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Relative frequency ($f_i$)
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Cumulative absolute frequency ($N_i$)
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Percentage ($\%$)
A streaming platform analyses data from its teenage users to improve its algorithm. Classify the following variables collected in the study: a) Number of devices…
A streaming platform analyses data from its teenage users to improve its algorithm. Classify the following variables collected in the study:
- a) Number of devices connected simultaneously in the household.
- b) Favourite film genre (horror, comedy, action, etc.).
- c) Total weekly viewing time (in hours and minutes).
- d) Rating given to a series (1 star, 2 stars, 3 stars, 4 stars or 5 stars).
- e) Brand of the main device used to watch content.
Explain whether any of these quantitative variables could be treated as qualitative in a given context.
Back to the beginning: In the cycle lane study, the population is all the young people in the city, the sample is the young people surveyed at random and the variable is the weekly frequency of use (discrete quantitative).