Questions: In statistics, you will need to evaluate expressions such as the one below. Evaluate the sum and round your final answer to 2 decimal places: (3(85)+5(90)+4(80)+6(82)+2(78))/(3+5+4+6+2)

Solution Steps

To evaluate the given expression, we need to calculate the weighted sum of the numbers in the numerator and then divide it by the total sum of the weights in the denominator. Finally, we round the result to two decimal places.

To find the weighted sum, we multiply each value by its corresponding weight and sum the results: \[ 3 \times 85 + 5 \times 90 + 4 \times 80 + 6 \times 82 + 2 \times 78 = 255 + 450 + 320 + 492 + 156 = 1673 \]

Sum the weights: \[ 3 + 5 + 4 + 6 + 2 = 20 \]

Divide the weighted sum by the total weight to find the average: \[ \frac{1673}{20} = 83.65 \]

Final Answer