Analyzing Variables: Quantitative vs

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School

TAFE NSW - Sydney Institute *

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CHC40221

Subject

Economics

Date

Jun 13, 2024

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docx

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Uploaded by DoctorKookabura3007

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?

- **Explanation**: The store might use this method to make the discount sound more appealing and substantial. It can create a psychological impression that the total discount is larger than it actually is when applied sequentially rather than as a single combined discount.

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