Question

sanibel island is known for having one of north americas best beaches for collecting shells. an oceanographer wants to determine the average weight, in ounces, of shells found on the sanibel island beach. he randomly collects and weighs shells over several days. this line plot shows the mean weight for each days collection of shells: line plot image based on these statistics, what is the best estimate for the average weight of a shell collected on the sanibel island beach? complete the sentence. the average weight of a shell is likely about, though the actual average weight could reasonably be anywhere between.

Explanation:

Step1: Count data points

Count: 2 at 8, 2 at 9, 1 at 9.5, 2 at 10, 1 at 10.5, 1 at 11, 7 at 11, 1 at 12, 2 at 13, 1 at 14. Total: 23 points.

Step2: Calculate total weight

$$(2\times8)+(2\times9)+(1\times9.5)+(2\times10)+(1\times10.5)+(1\times11)+(7\times11)+(1\times12)+(2\times13)+(1\times14) = 230$$

Step3: Compute mean weight

$$\text{Mean} = \frac{230}{23} = 10$$

Step4: Identify reasonable range

The data clusters between 8 and 12 ounces, so this is the reasonable range for the true average.

Answer:

The average weight of a shell is likely about 10 ounces, though the actual average weight could reasonably be anywhere between 8 ounces and 12 ounces.