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A survey of young people's shopping habits in a small city during the summer months of 2015 showed the following: Shoppers aged 12 to 14 years took an average of 8 shopping trips per month and spent an average of \(\$ 14\) per trip. Shoppers aged 15 to 17 years took an average of 11 trips per month and spent an average of \(\$ 18\) per trip. Assume that this city has 1100 shoppers aged 12 to 14 years and 900 shoppers aged 15 to 17 years. a. Find the total amount spent per month by all these 2000 shoppers in both age groups. b. Find the mean number of shopping trips per person per month for these 2000 shoppers. c. Find the mean amount spent per person per month by shoppers aged 12 to 17 years in this city.

Step by step solution

01

Calculate the Total Amount Spent per Month by All Shoppers

First, calculate the total number of shopping trips and total amount spent by each age group per month. This can be done by multiplying the average number of trips by the average amount spent per trip, and then by the number of shoppers. So for the 12-14 age group, it would be: 8 (average trips) x \$14 (average spending per trip) x 1100 (number of shoppers) = \$123,200. Similarly, for the 15-17 age group, it would be: 11 (average trips) x \$18 (average spending per trip) x 900 (number of shoppers) = \$178,200. Add these two amounts together to get the total amount spent per month by all shoppers.

02

Calculate the Mean Number of Shopping Trips

In this step, calculate the mean number of trips per person by adding the products of the average number of shopping trips and the number of shoppers in each age group, and then dividing this sum by the total number of shoppers. This can be calculated by the formula: \(\frac{(8 \times 1100 + 11 \times 900)}{2000}\).

03

Calculate the Mean Amount Spent per Person per Month

In the last step, calculate the mean amount spent per person by dividing the total amount spent (as calculated in step 1) by the total number of shoppers. Use this formula: \(\frac{\$301,400}{2000}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mean Calculation

Calculating the mean is a foundational skill in statistics. It's often the first step in understanding a collection of numbers. In this exercise, we began by finding the total spending for a group of shoppers. To do this, we calculated the mean number of shopping trips and spending for each age group.
To find the total amount spent, you multiply the average trips by the average cost per trip and then by the number of shoppers. For instance:

• Ages 12-14: 8 trips x $14 x 1100 shoppers = $123,200
• Ages 15-17: 11 trips x $18 x 900 shoppers = $178,200

By summing these totals, you get the aggregate spending. These calculations demonstrate the power of the mean for summarizing spending patterns across different groups.

Survey Analysis

Survey analysis is a powerful tool to understand consumer behaviors and preferences. In this case, the survey focuses on young people's shopping habits, revealing patterns in how frequently they shop and how much they spend.
The survey provided average data, which is crucial for interpreting the shopping tendencies of these age groups. By analyzing these averages, we can make informed decisions about store inventory, marketing strategies, or city planning initiatives.
In a survey:

• Data collection involves understanding the demographic characteristics.
• Analyzing averages helps in identifying typical behaviors.
• Insights derived guide future strategies and initiatives.

Shopping Habits

Shopping habits among different age groups reveal how spending patterns evolve. Understanding these habits can influence everything from product placement to promotional events.
Shoppers aged 12-14 years averaged 8 trips per month with spending per trip at $14. Older teens, aged 15-17 years, showed a different pattern with 11 trips per month and spending $18 per trip.
Key insights into shopping habits include:

• Younger teens shop less frequently but may have more impactful purchases per trip.
• Older teens shop more frequently, suggesting a greater need for products targeting daily use.
• Identifying these patterns helps businesses tailor their offerings to meet consumer demands.

Data Interpretation

Interpreting data is about making sense of numbers to tell a story. From the given statistics, we calculated the averages and derived meaningful conclusions about shopping behaviors. This process involves taking raw data and transforming it into actionable insights.
To interpret the data:

• Calculate totals and averages to uncover underlying patterns and trends.
• Use these calculations to understand overall behaviors, such as total spending or frequency of shopping.
• Apply insights to practical decisions, such as adjusting marketing strategies or stocking inventory.

These interpretations provide a snapshot of consumer habits that can be leveraged to improve customer satisfaction and business success.