What is Data?

Data is a collection of facts, numbers, or information used for analysis. It helps us understand patterns, make predictions, and solve problems.

Questions

Criterion A: Knowing and Understanding

Question 1: Define categorical data and numerical data with examples.

Question 2: Identify whether the following data types are categorical or numerical:

• The number of goals scored in a football match.

• The different types of cuisines people like.

• The heights of students in centimeters.

• The brands of mobile phones people use.

Question 3: Explain why we cannot calculate an average for categorical data but can for numerical data.

Criterion D: Applying Mathematics in Real-Life Contexts

Question 4: A company wants to conduct a survey to improve its product. They decide to ask the following questions:

• “What is your age?”

• “Which brand of laptop do you use?”

• “How many hours do you use your laptop daily?”

• “Do you prefer Windows or MacOS?”

• “Rate your satisfaction with your laptop from 1 to 10.”

a) Identify which questions collect categorical data and which collect numerical data.
b) How can the company use this data to make better decisions?

Question 5: A restaurant manager collects data on customers’ favorite pizza toppings and the number of pizzas sold daily:

• Which type of data is pizza topping preference?

• Which type of data is the number of pizzas sold?

• Suggest a way the restaurant can use this data for business improvement.

Answers

Criterion A: Knowing and Understanding

Answer 1: Categorical data consists of names, labels, or categories (e.g., favorite color, type of pet, car brand).
Numerical data consists of numbers that can be measured or counted (e.g., height in cm, number of siblings, test scores).

Answer 2: Categorical or Numerical Data:

• The number of goals scored in a football match. (Numerical data)

• The different types of cuisines people like. (Categorical data)

• The heights of students in centimeters. (Numerical data)

• The brands of mobile phones people use. (Categorical data)

Answer 3: Why we cannot calculate an average for categorical data:

• Categorical data represents labels or categories without a numerical value, so averaging does not make sense. For example, you cannot find the average of ‘red, blue, and green.’

• Numerical data consists of numbers that can be added and divided, making it possible to find an average (e.g., the average height of students).

Criterion D: Applying Mathematics in Real-Life Contexts

Answer 4: Company survey data types:

• “What is your age?” (Numerical)

• “Which brand of laptop do you use?” (Categorical)

• “How many hours do you use your laptop daily?” (Numerical)

• “Do you prefer Windows or MacOS?” (Categorical)

• “Rate your satisfaction with your laptop from 1 to 10.” (Numerical)

b) The company can analyze numerical data to see trends (e.g., average laptop usage) and categorical data to understand brand preference. This helps in marketing and improving products.

Answer 5: Restaurant data analysis:

• Pizza topping preference → Categorical (e.g., Pepperoni, Cheese, Veggie, BBQ Chicken).

• Number of pizzas sold → Numerical (countable data).

• Business improvement suggestion: The restaurant can analyze popular toppings to optimize inventory and create targeted promotions.