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A sample of 38 customers was taken at a computer store. Each customer was asked the price of the computer they bought. Here is a summary.
\begin{tabular}{|c|c|} \hline Number of computers & \begin{tabular}{c} Price paid for each \\ (in dollars) \end{tabular} \\ \hline 6 & 900 \\ \hline 18 & 1050 \\ \hline 14 & 2600 \\ \hline \end{tabular}
Find the mean price for this sample. Round your answer to the nearest dollar.
To find the mean price for the sample of computers, you need to follow these steps:
1. Multiply the price paid for each computer by the number of computers bought at that price to find the total cost for each price segment:
- For the 6 computers bought at [tex]$900 each:
\[
6 \times 900 = 5400
\]
- For the 18 computers bought at $[/tex]1050 each: [tex]\[
18 \times 1050 = 18900
\][/tex]
- For the 14 computers bought at [tex]$2600 each:
\[
14 \times 2600 = 36400
\]
2. Sum the total costs from each price segment to find the total cost for all computers:
\[
5400 + 18900 + 36400 = 60700
\]
3. Sum the total number of computers:
\[
6 + 18 + 14 = 38
\]
4. Divide the total cost by the total number of computers to find the mean price:
\[
\text{Mean price} = \frac{60700}{38} \approx 1597.368
\]
5. Round the mean price to the nearest dollar:
\[
\text{Mean price} \approx 1597
\]
Thus, the mean price of the computers in the sample, rounded to the nearest dollar, is $[/tex]1597.
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