A sample mean is the average of the trees counted, used to estimate the average per tree across the whole orchard. For raw counts, put every count in a Desmos list and use , then multiply by the number of trees in the orchard. The sample size tells you how many counts to average, not how many trees to use for the estimated total.
Hints
- Hint 1
The mean is the total of the sample counts divided by the number of sampled trees. Put the counts in a Desmos list, including both entries of . What does the mean tell you about one tree?
- Hint 2
A sample is the smaller group measured to estimate the whole orchard. Once you have an estimate of apples per tree, multiply by all trees, not by the eight trees you counted.
Step-by-step
Use the sample mean to estimate the orchard total
Step 1Find the average apples per sampled tree
The mean is the total of the counts divided by how many counts there are. Type , then . Keep both entries of in the list. Desmos shows apples per sampled tree.
- Step 2
Connect the per-tree mean to the orchard total
Multiply the estimated apples per tree by all trees, not the eight sampled trees. So if is the estimated total number of apples, . The eight counts determine the average; they aren't the number of trees in the orchard.
- Step 3
Calculate and match the range
Type in Desmos. It shows , the estimated total number of apples. That falls between and apples. Choice C.