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가중평균 계산기

Weighted average calculator: enter values with weights, one pair per line, for the weighted mean, sum of weights and each value's contribution.

업데이트 검증한 예제: 7

One pair per line: the value, then its weight. Separate them with a space, comma or tab, and don't use thousands separators. A label in front is optional.
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가중평균
가중평균: 82.9
최대 소수 자릿수: 6; 가장 가까운 값, 중간값은 0에서 먼 쪽으로
Sum of weights
100%
Sum of value × weight
8,290
Number of values
3
Unweighted average
85

The weighted average is 82.9: the products add up to 8,290 and the weights to 100. The unweighted average is 85; Final exam, with the largest weight (50% of the total), pulls the result down toward 78.

What each value adds to the weighted average

Homework18.4Midterm25.5Final exam39

Share of the total weight

82.9weighted average
Homework20%Midterm30%Final exam50%
Each value's share 행 수: 3
Item값WeightShare of weightValue × weightContribution
Homework922020 %1,84018.4
Midterm853030 %2,55025.5
Final exam785050 %3,90039
계산 방법 S

  1. Multiply each value by its weight

    92×20=1,84085×30=2,55078×50=3,900\begin{aligned} 92 \times 20 &= 1{,}840 \\ 85 \times 30 &= 2{,}550 \\ 78 \times 50 &= 3{,}900 \end{aligned}

  2. Add the products and the weights

    ∑wx=1,840+2,550+3,900=8,290∑w=20+30+50=100\sum wx = 1{,}840 + 2{,}550 + 3{,}900 = 8{,}290 \qquad \sum w = 20 + 30 + 50 = 100

  3. Divide

    xˉw=∑wx∑w=8,290100=82.9\bar x_w = \frac{\sum wx}{\sum w} = \frac{8{,}290}{100} = 82.9

  4. Compare with the unweighted average

    xˉ=∑xn=2553=85\bar x = \frac{\sum x}{n} = \frac{255}{3} = 85

    Weighting moves the average down by 2.1.

가중평균 계산기 소개

A weighted average multiplies each value by its weight, adds the products and divides by the sum of the weights: Σwx ÷ Σw. Values with larger weights pull the result toward themselves, and with equal weights it is the ordinary mean.

Course grades are the usual case. With homework at 92 counting 20%, the midterm at 85 counting 30% and the final at 78 counting 50%, the products add up to 8,290 and the weights to 100, so the weighted average is 82.9, while the plain average of the three scores is 85. Weights can be credits for a GPA, share counts for an average purchase price, or any relative importance.

Weights only need to be in proportion: 20%, 30% and 50% give the same answer as 2, 3 and 5. They must not be negative, and at least one must be above zero. A label before the numbers on a line, such as “Final exam”, is carried into the table.

계산 예제

Course grade (default)

Values and weights
Homework 92 20% Midterm 85 30% Final exam 78 50%
가중평균
82.9
Sum of weights
100 %
Sum of value × weight
8,290
Number of values
3
Unweighted average
85

검증 출처: Hand calculation: (92 × 20 + 85 × 30 + 78 × 50) / 100 = 8290 / 100 = 82.9

GPA by credit hours (Inch Calculator example)

Values and weights
3.0 4 4.0 3 3.7 4 3.3 3
가중평균
3.48
Sum of weights
14
Sum of value × weight
48.7

검증 출처: Inch Calculator weighted average page: (3.0×4 + 4.0×3 + 3.7×4 + 3.3×3) / 14 = 48.7 / 14, GPA 3.48

GPA with four classes (Omni Calculator example)

Values and weights
A 4 4 B 3 4 A 4 3 C+ 2.3 2
가중평균
3.430769
Sum of weights
13
Sum of value × weight
44.6
Unweighted average
3.325

검증 출처: Omni Calculator weighted average page: (4·4 + 3·4 + 4·3 + 2.3·2) / 13 = 3.43; Python Fraction(446, 130) = 3.4307692…

Average share price

Values and weights
100 10 110 20
가중평균
106.666667
Sum of value × weight
3,200
Sum of weights
30
Unweighted average
105

검증 출처: Hand calculation: (100 × 10 + 110 × 20) / 30 = 3200 / 30 = 106.67

자주 묻는 질문

How do you calculate a weighted average?

Multiply each value by its weight, add the products, and divide by the total weight. For scores of 92, 85 and 78 weighted 20%, 30% and 50%: 92 × 20 + 85 × 30 + 78 × 50 = 8,290, and 8,290 ÷ 100 = 82.9. In a spreadsheet the same formula is =SUMPRODUCT(values, weights)/SUM(weights).

Do the weights have to add up to 100%?

No. Dividing by the sum of the weights rescales them automatically, so weights of 2, 3 and 5 give the same result as 20%, 30% and 50%. If percentage weights add up to 90% because a grade item is still missing, the result is the average of the work done so far, with each item's weight divided by 0.9.

How do you calculate a weighted GPA?

Use the grade points as values and the credit hours as weights. For a B (3.0) in a 4-credit class, an A (4.0) in 3 credits, an A− (3.7) in 4 credits and a B+ (3.3) in 3 credits, the quality points are 12 + 12 + 14.8 + 9.9 = 48.7 over 14 credits, a GPA of 3.48. The GPA calculator converts letter grades for you.

What is the difference between a weighted average and a simple average?

A simple average gives every value the same weight, 1/n. A weighted average lets some values count more. For the default grades the simple average is (92 + 85 + 78) ÷ 3 = 85, but the final exam, worth half the grade, pulls the weighted average down to 82.9. The two agree only when all weights are equal.

How do you find the average price of shares bought at different prices?

Weight each price by the number of shares bought at it. Buying 10 shares at $100 and 20 at $110 costs $1,000 + $2,200 = $3,200 for 30 shares, an average of $106.67 per share, not the $105 you get by averaging the two prices. This weighted average is the cost basis per share used to work out a gain or loss.

“가중평균 계산기”의 정확도는 어느 정도인가요?

정확도는 입력값과 계산 방법의 가정에 따라 달라집니다. 십진 연산은 유효숫자 50자리를 사용하지만, 추정값·수치해석 방법·원본 데이터의 정밀도는 더 낮을 수 있습니다. 표시값을 반올림해도 이러한 한계는 사라지지 않습니다. 독립적인 출처의 풀이와 대조한 계산 예시: 7. 예를 들어 “Course grade (default)”은 Hand calculation: (92 × 20 + 85 × 30 + 78 × 50) / 100 = 8290 / 100 = 82.9와 대조해 확인합니다.

이 계산 방법의 출처는 무엇인가요?

Wolfram MathWorld: Weighted mean; NIST Dataplot reference manual: WEIGHTED SUM (Σ wᵢxᵢ).

이 계산기 소개

xˉw=∑i=1nwixi∑i=1nwi\bar x_w = \frac{\sum_{i=1}^{n} w_i x_i}{\sum_{i=1}^{n} w_i}

출처

  1. Wolfram MathWorld: Weighted mean
  2. NIST Dataplot reference manual: WEIGHTED SUM (Σ wᵢxᵢ)

출처와 대조하여 검증

이 계산기에는 독립적인 출처에서 답을 얻은 계산 예제가 7개 있습니다. 테스트 모음에서 실행되며 여기에서도 실행할 수 있습니다.

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