Let's solve the problem step-by-step:
Step 1: Calculate the total number of computers.
We are given a breakdown of the number of computers sold at different price points:
- 6 computers were sold at [tex]$900 each.
- 18 computers were sold at $[/tex]1050 each.
- 14 computers were sold at [tex]$2600 each.
To find the total number of computers sold, sum these values:
\[ \text{Total computers} = 6 + 18 + 14 = 38 \]
Step 2: Calculate the total cost of all computers sold.
Next, we need to calculate the total cost for each price point and then sum those costs.
- For the 6 computers at $[/tex]900 each:
[tex]\[ 6 \times 900 = 5400 \][/tex]
- For the 18 computers at [tex]$1050 each:
\[ 18 \times 1050 = 18900 \]
- For the 14 computers at $[/tex]2600 each:
[tex]\[ 14 \times 2600 = 36400 \][/tex]
Now, we sum these total costs to get the overall total cost:
[tex]\[ \text{Total cost} = 5400 + 18900 + 36400 = 60700 \][/tex]
Step 3: Calculate the mean price per computer.
The mean price per computer is obtained by dividing the total cost by the total number of computers:
[tex]\[ \text{Mean price} = \frac{\text{Total cost}}{\text{Total computers}} = \frac{60700}{38} \approx 1597.3684210526317 \][/tex]
Step 4: Round the mean price to the nearest dollar.
Finally, we round the calculated mean price to the nearest dollar:
[tex]\[ \text{Rounded mean price} \approx 1597 \][/tex]
Answer:
The mean price for this sample, rounded to the nearest dollar, is \$1597.
