Statistics concepts

A video game company wants to know what the favorite genre of students at your school is. In order not to ask all $800$ students, they decide to survey $10$ students from each class in the school.

Identify the following elements of the statistical study:

• Population:

• Sample:

• Individual:

To improve the quality of the food in the cafeteria of a large high 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:

• a) Population.

• b) Sample.

• c) Individual.

A famous influencer wants to know what Dominican teenagers think about the new time limit on a social media platform. To do this, they post a poll on their Instagram "stories" for 24 hours. $15,400$ people take part.

1. a) Identify the population under study and the sample used.
2. b) Do you think the sample is representative of the population? Reason your answer by analyzing two possible factors that could invalidate the results (biases).
3. c) Propose a more reliable method for choosing a sample of $500$ individuals that truly represents all teenagers in the Dominican Republic.

Classify the following statistical variables as qualitative (if they express a quality or characteristic) or quantitative (if they are expressed by a number):

1. a) The names of the most used apps on your friends' cell phones.
2. b) The number of siblings each student in your class has.
3. c) The brand of sneakers worn by the players on a team.
4. d) The maximum temperature reached in your city each day of this week.
5. e) The favorite sport of the members of a track and field club.

Within quantitative variables, we distinguish between discrete (when they take isolated values, usually whole numbers) and continuous (when they can take any value in an interval, such as decimals). Classify these variables:

1. a) The number of goals scored by a team in each league game.
2. b) The exact time taken by a swimmer to cover $50$ meters.
3. c) The number of books in the students' backpacks.
4. d) The height of the players on the Dominican national basketball team.

A well-known streamer wants to know what their followers' favorite video game in the Dominican Republic 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 favorite 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.

An online clothing store wants to know the level of satisfaction of its customers (Very dissatisfied, Dissatisfied, Neutral, Satisfied, Very satisfied).

• a) Classify this variable. Is it quantitative or qualitative?

• b) Although words are used, sometimes numbers ($1$ to $5$) are assigned to calculate the mean. Do you think this turns the variable into a quantitative one? Reason your answer.

• c) If the store sends the survey to $500$ customers who bought something yesterday, who is the "individual" in this study?

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 postal code of the residence of students at a high school.
2. b) The serial number of the computers in the library.
3. c) The daily mean temperature recorded in the schoolyard during the month of January.
4. d) The jersey number of the players on a basketball team.
5. e) The time, expressed in seconds, taken by a group of swimmers to cross a $50$-meter swimming pool.

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

A group of friends is discussing which film to go and see at the cinema. They have written down their preferences:

Adventure, Comedy, Horror, Adventure, Adventure, Horror, Comedy, Adventure, Comedy.

Answer the following questions on the basic concepts:

1. a) What is the statistical variable being studied?
2. b) What type of variable is it?
3. c) What is the absolute frequency (number of times it appears) of the category "Adventure"?

Look at the following bar chart representing the pets of the students in a class and answer based on the concepts learned:

1. a) What is the sample size (total number of students surveyed)?
2. b) What is the variable studied and what type is it?
3. c) What is the absolute frequency of the variable value "Cat"?

You can do it on paper and send a photo with your answer.

In a study on fruit consumption in a class of $30$ students, some data from the frequency table have been lost. We know that the relative frequency ($h_i$) of students who eat "3 pieces a day" is exactly $0.2$ and that the absolute frequency ($f_i$) of those who eat "1 piece a day" is three times that of those who eat "none".

If $2$ students do not eat any pieces of fruit a day, complete the following data with reasoning:

1. a) How many students eat $3$ pieces of fruit a day?
2. b) How many students eat $1$ piece of fruit a day?
3. c) What is the absolute frequency of those who eat "2 pieces a day", knowing that all the above options add up to the class total?

A survey was conducted on the number of children per family in a residential development of $200$ families. It is known that $15\%$ of the families have $3$ or more children.

1. a) What is the absolute frequency of the event "having 3 or more children"?
2. b) If the angle in a circle graph for families with "1 child" is $144^\circ$, how many families have exactly one child?
3. c) Calculate the relative frequency of the group of families that have "1 child".

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 $3$ movie tickets will cost if each one is worth $480$ pesos.
3. c) Asking a classmate what their favorite color is.
4. d) Dropping a stone from a balcony and seeing if it falls downward.
5. e) Drawing a card from a Spanish deck of cards without looking.

State whether the following phenomena are random or deterministic, briefly justifying your answer:

• a) Knowing whether it will rain in your city on the exact day of your birthday next year.

• b) Calculating the price of $5$ movie tickets if you know that each one costs $510$ pesos.

• c) Predicting the number that will come up when rolling a 10-sided die in a role-playing game.

• d) Knowing the grade on a math test if you have left all the questions blank.

• e) Drawing a card from a Spanish deck of cards and getting the Ace of Coins.

Identify whether the following phenomena are random or deterministic, explaining why in each case. For random phenomena, describe their sample space:

1. a) Dropping a stone from a balcony and timing how long it takes to reach the ground (assuming there is no wind and the height is fixed).
2. b) The number that will win the top prize in the Christmas lottery drawing.
3. c) Drawing a card from a Spanish deck of cards and observing whether it is a "picture card" (Jack, Knight, or King).
4. d) Mixing an acid with a base in a chemistry laboratory following an exact ratio to produce a salt.
5. e) The exact time it will take for the next bus to arrive at the stop.