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Zorluk: OrtaWeighted Average and Combined Sets

A citrus orchard harvested two varieties of oranges: Valencia and Navel. The harvest consisted of 800800 crates of Valencia oranges with an average weight of 4545 pounds per crate, and 1,2001,200 crates of Navel oranges with an average weight of 5050 pounds per crate. What is the average weight, in pounds per crate, for the combined harvest of all crates?

Cevap: 48 pounds per crate

Cevap

The average weight of the combined harvest is 48 pounds per crate.
The weighted average is found by calculating the total overall weight divided by the total number of crates. Since Valencia oranges account for 36,000 pounds (800 crates at 45 lbs/crate) and Navel oranges account for 60,000 pounds (1,200 crates at 50 lbs/crate), the total weight is 96,000 pounds across 2,000 crates. Dividing 96,000 by 2,000 gives exactly 48 pounds per crate.

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1
Calculate the total weight contributed by each variety of oranges.
Valencia weight = 800×45=36,000800 \times 45 = 36,000 lbs; Navel weight = 1,200×50=60,0001,200 \times 50 = 60,000 lbs.
Total weight equals the product of the number of units and the average weight per unit for each group.
2
Determine the total combined weight and the total number of crates.
Total weight = 36,000+60,000=96,00036,000 + 60,000 = 96,000 lbs; Total crates = 800+1,200=2,000800 + 1,200 = 2,000 crates.
Combined weighted averages require summing total values across all subsets.
3
Divide total weight by total number of crates to find the overall weighted average.
Weighted average = 96,0002,000=48\frac{96,000}{2,000} = 48 lbs per crate.
Weighted mean formula: xˉ=∑(ni⋅xi)∑ni\bar{x} = \frac{\sum (n_i \cdot x_i)}{\sum n_i}.

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Weighted Average of Combined Sets
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Weighted Average and Combined Sets

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