Final answer:
The weighted mean of the numbers 12, 23, 27, 59, and 74 with respective weights of 14% for the first two and 8.7% for the last three is approximately 34.8 when rounded to the tenths.
Step-by-step explanation:
The question is asking to find the weighted mean of a set of numbers with given weights. The weights given are 14% for the first two numbers (12 and 23) and 8.7% for the last three numbers (27, 59, and 74). The weighted mean is calculated by multiplying each number by its respective weight, summing these products, and then dividing by the sum of the weights.
Here's how the calculation is done:
(12 × 0.14) + (23 × 0.14) = 1.68 + 3.22 = 4.9 (Weighted sum for the first two numbers)
(27 × 0.087) + (59 × 0.087) + (74 × 0.087) = 2.349 + 5.133 + 6.438 = 13.92 (Weighted sum for the last three numbers)
Total weighted sum = 4.9 + 13.92 = 18.82
Total weight = (2 × 0.14) + (3 × 0.087) = 0.28 + 0.261 = 0.541
Weighted mean = Total weighted sum ÷ Total weight = 18.82 ÷ 0.541 ≈ 34.8 (rounded to the tenths)
Therefore, the weighted mean of the numbers is approximately 34.8 when rounded to the tenths.