Statistical concepts

Many things happen in our daily lives, but not all of them depend on chance. State which of the following situations are random experiments and which are deterministic:

1. a) Tossing a coin and seeing whether it lands on heads or tails.
2. b) Calculating how much $3$ cinema tickets will cost if each one is worth $8$ euros.
3. c) Asking a classmate what their favourite colour is.
4. d) Dropping a stone from a balcony and seeing if it falls downwards.
5. e) Drawing a card from a Spanish deck of cards without looking.

A well-known streamer wants to know what their followers' favourite video game in Spain is. To do this, they conduct a quick poll during a livestream in which $1500$ people participate. Classify the following variables collected in the study as qualitative or quantitative:

• a) Title of the favourite video game.

• b) Number of hours they play per week.

• c) Console or platform used (PC, PS5, Switch, etc.).

• d) Amount of money spent on "skins" or battle passes per month.

• e) Rating of the livestream from 1 to 10.

Among quantitative variables, we distinguish between discrete ones (when they take isolated values, usually whole numbers) and continuous ones (when they can take any value in an interval, such as decimals). The figure shows the difference: above, isolated values; below, a stretch of the line in which any value fits, including decimals.

Classify these variables as discrete or continuous:

1. a) The number of goals a team scores in each league match.

1. b) The exact time a swimmer takes to cover $50$ meters.

1. c) The number of books in the students' backpacks.

1. d) The height of the members of the Spanish national basketball team.

To improve the quality of the food in the cafeteria of a large school with $1200$ students, the school board decides to ask the opinion of the first $5$ students from each class who enter the school on Monday morning. Identify the following elements of this statistical study:

1. a) Population.

1. b) Sample.

1. c) Individual.

Classify the following statistical variables as qualitative or quantitative. In the case of quantitative variables, reflect on whether it makes sense to perform arithmetic operations (such as the mean) with their values:

1. a) The postcode of the residence of students at a secondary school.
2. b) The serial number of the computers in the library.
3. c) The daily mean temperature recorded in the school playground during the month of January.
4. d) The shirt number of the players in a basketball team.
5. e) The time, expressed in seconds, taken by a group of swimmers to cross a $50$-metre swimming pool.

Note: Think about whether the "number" acts as a label or as a real measurement.