Analyzing Variables: Quantitative vs
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Jun 13, 2024
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Let's analyze and solve the questions in the image.
### Question 1: For each of the following variables, indicate whether it is quantitative or categorical. Then, identify the individual (or case) and write a sentence explaining why you might be interested in such a variable.
#### a. The number of calories in a cup of breakfast cereal
- **Type**: Quantitative
- **Individual**: A cup of breakfast cereal
- **Interest**: This variable is important for nutritional analysis and diet planning, helping individuals manage their calorie intake.
#### b. Salaries of last year's college graduates
- **Type**: Quantitative
- **Individual**: Last year's college graduates
- **Interest**: Understanding salary ranges can provide insights into job market trends and help new graduates set salary expectations.
#### c. Preferred brand of cola
- **Type**: Categorical
- **Individual**: Consumers
- **Interest**: Companies can use this information for market research to identify popular brands and tailor their marketing strategies.
#### d. Time it takes college freshmen to read a particular editorial
- **Type**: Quantitative
- **Individual**: College freshmen
- **Interest**: This data can be used to study reading comprehension and speed, which can help in developing educational programs.
#### e. Race of small business owners in Philadelphia
- **Type**: Categorical
- **Individual**: Small business owners in Philadelphia
- **Interest**: This information is useful for demographic studies and can help in creating policies to support diversity in business ownership.
### Question 2: A store advertises its discounts in two parts. Here is the offer: "Take 50% off of the original price, then take another 30% off of that." Suppose a shirt you want to buy originally cost $25.00.
#### a. If there is a single discount of 50%, how much would the shirt cost?
- **Calculation**: \( 25.00 \times 0.50 = 12.50 \)
- **Answer**: $12.50
#### b. If we now apply the second discount of 30% to the discounted price of the shirt from part (a), what is the cost?
- **Calculation**: \( 12.50 \times 0.70 = 8.75 \)
- **Answer**: $8.75
#### c. With the "double discount" as described, what is the total percentage discount deducted from the original price?
- **Calculation**: First discount: 50%, second discount on the reduced price: \( 50\% + (0.50 \times 30\%) = 50\% + 15\% = 65\% \)
- **Answer**: 65%
#### d. Would that "double discount" percentage be the same for an item with a different original price? Explain your answer.
- **Explanation**: Yes, the percentage discount would remain the same because the discounts are applied multiplicatively. The sequence of applying 50% followed by 30% on the new price remains consistent regardless of the original price.
#### e. Why do you think the store uses this two-part advertising method?
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