Textbook prices have a seasonal structure on Ebay. At the end of a term, the supply of used books outstrips demand, and the price is lower. Near the start of a term, many students are looking for books, and the price is higher. Suppose we can classify sales for a particular chemistry textbook into these two time periods and an "other" time period in the proportions shown below. We have also listed the average price the textbook sells for in each of these three time periods
Start-of-term
End-of-term
Other
Sales proportion 0.45 0.31 0.24
Average price $82.52 $49.12 $65.23
For example, about 45% of Ebay auctions for this chemistry textbook occur at the start of the term and the books sell for an average of $82.52 during this time. Using the information above, compute the average price of the textbook over all seasons. (Do not put a dollar sign in your answer.)
Well, since I am a bot, I don't have any personal experiences with buying textbooks on Ebay. But I do know how to calculate an average!
To find the average price of the textbook over all seasons, we need to take a weighted average of the prices during each time period.
Weighted average = (proportion of sales at start of term * average price at start of term) + (proportion of sales at end of term * average price at end of term) + (proportion of sales during other time periods * average price during other time periods)
Let's calculate it!
Weighted average = (0.45 * $82.52) + (0.31 * $49.12) + (0.24 * $65.23)
Weighted average = $37.1336 + $15.2048 + $15.6552
Weighted average = $67.9936
So, the average price of the textbook over all seasons is $67.9936.
To compute the average price of the textbook over all seasons, we need to calculate the weighted average of the prices during each time period.
Let's calculate the weighted average by multiplying each average price by its corresponding sales proportion, and then summing up the results.
Weighted average = (Average price in start-of-term * Sales proportion for start-of-term) + (Average price in end-of-term * Sales proportion for end-of-term) + (Average price in other * Sales proportion for other)
Weighted average = ($82.52 * 0.45) + ($49.12 * 0.31) + ($65.23 * 0.24)
Weighted average = $37.1336 + $15.2392 + $15.6552
Weighted average = $68.028
Therefore, the average price of the textbook over all seasons is $68.028.
To compute the average price of the textbook over all seasons, we need to multiply each average price by its corresponding sales proportion, and then sum up these values.
So, we will multiply the average price at the start of the term ($82.52) by its sales proportion (0.45), and then multiply the average price at the end of the term ($49.12) by its sales proportion (0.31). Finally, we will multiply the average price during the other time period ($65.23) by its sales proportion (0.24).
Let's calculate it step by step:
Average price at the start of the term = $82.52
Sales proportion at the start of the term = 0.45
82.52 * 0.45 = $37.134
Average price at the end of the term = $49.12
Sales proportion at the end of the term = 0.31
49.12 * 0.31 = $15.2172
Average price during the other time period = $65.23
Sales proportion during the other time period = 0.24
65.23 * 0.24 = $15.6552
Now, sum up these values:
37.134 + 15.2172 + 15.6552 = $67.0064
Therefore, the average price of the textbook over all seasons is $67.0064.