Lucila wondered what the average weight of each grapefruit was in a five-pound bag of grapefruits. She purchased six bags and calculated the average weight for a single grapefruit in each bag.
| Bag of Grapefruits | Average Grapefruit Weight (oz) |
| ------------------ | ------------------------------ |
| 1 | 7.1 |
| 2 | 6.9 |
| 3 | 7.3 |
| 4 | 7.6 |
| 5 | 8.1 |
| 6 | 7.5 |
Using her results, a grapefruit from a five-pound bag of grapefruits should weigh between
A. 7.3 oz and 7.6 oz .
B. 7.1 oz and 7.5 oz .
C. 6.9 oz and 8.1 oz .
D. 7.1 oz and 7.6 oz .
Answer (1)
Calculate the overall average weight of a grapefruit: 6 7.1 + 6.9 + 7.3 + 7.6 + 8.1 + 7.5 = 7.416666... ≈ 7.42 oz.
Identify the minimum average weight: 6.9 oz.
Identify the maximum average weight: 8.1 oz.
Determine the range based on the minimum and maximum weights: 6.9 oz and 8.1 oz .
Explanation
Understanding the Problem Lucila wants to estimate the average weight of a grapefruit from a five-pound bag based on the average weights she found in six different bags. We need to determine the range within which a grapefruit's weight should fall, based on her data.
Calculating the Overall Average First, let's calculate the overall average weight by averaging the average weights from the six bags. The weights are 7.1 oz, 6.9 oz, 7.3 oz, 7.6 oz, 8.1 oz, and 7.5 oz.
Summing the Weights The sum of the weights is 7.1 + 6.9 + 7.3 + 7.6 + 8.1 + 7.5 = 44.5 oz.
Finding the Average Weight To find the average, we divide the sum by the number of bags, which is 6: 6 44.5 = 7.416666... oz. So, the overall average weight is approximately 7.42 oz.
Identifying Minimum and Maximum Weights Next, we need to identify the minimum and maximum average weights from the six bags. The minimum weight is 6.9 oz, and the maximum weight is 8.1 oz.
Determining the Range Therefore, based on Lucila's results, a grapefruit from a five-pound bag should weigh between 6.9 oz and 8.1 oz.
Selecting the Correct Option Comparing this range with the provided options, the correct answer is:
9 oz and 8.1 oz .
Examples
Understanding the average weight of fruits can be useful in various real-life scenarios. For example, if you're running a grocery store, knowing the average weight of grapefruits helps in estimating the total weight of the stock and planning shelf space accordingly. Similarly, in agriculture, farmers can use this information to estimate the yield from their orchards and plan for transportation and storage. This concept is also applicable in logistics, where knowing the average weight of items helps in optimizing packaging and shipping costs.
