# وزنی اوسط کا کیلکولیٹر

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

انٹرایکٹو صورت: https://www.calcopenly.com/ur/math/weighted-average-calculator
موضوع: ریاضی کے کیلکولیٹر

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.

## اندراجات

- **Values and weights**: 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.

## نتائج

- وزنی اوسط — بنیادی نتیجہ
- Sum of weights
- Sum of value × weight
- Number of values
- Unweighted average

## فارمولا

$$
\bar x_w = \frac{\sum_{i=1}^{n} w_i x_i}{\sum_{i=1}^{n} w_i}
$$

## حل شدہ مثالیں

### Course grade (default)

- Values and weights: Homework 92 20% / Midterm 85 30% / Final exam 78 50%
- **وزنی اوسط: 82.9**
- **Sum of weights: 100 %**
- **Sum of value × weight: 8,290**
- **Number of values: 3**
- **Unweighted average: 85**
- جانچ کا ماخذ: ⁨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
- **وزنی اوسط: 3.48**
- **Sum of weights: 14**
- **Sum of value × weight: 48.7**
- جانچ کا ماخذ: ⁨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
- **وزنی اوسط: 3.430769**
- **Sum of weights: 13**
- **Sum of value × weight: 44.6**
- **Unweighted average: 3.325**
- جانچ کا ماخذ: ⁨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
- **وزنی اوسط: 106.666667**
- **Sum of value × weight: 3,200**
- **Sum of weights: 30**
- **Unweighted average: 105**
- جانچ کا ماخذ: ⁨Hand calculation: (100 × 10 + 110 × 20) / 30 = 3200 / 30 = 106.67⁩

### Equal weights give the plain mean

- Values and weights: 10 1 / 20 1 / 30 1
- **وزنی اوسط: 20**
- **Unweighted average: 20**
- جانچ کا ماخذ: ⁨Definition: with wᵢ = 1 the weighted mean is Σx / n = 60 / 3⁩

### A zero weight drops the value (edge case)

- Values and weights: 50 0 / 80 1
- **وزنی اوسط: 80**
- **Sum of weights: 1**
- **Number of values: 2**
- **Unweighted average: 65**
- جانچ کا ماخذ: ⁨Definition: a value with weight 0 adds nothing to Σwx or Σw, so x̄ = 80 / 1⁩

## سوالات

### 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.

### “⁨وزنی اوسط کا کیلکولیٹر⁩” کتنا درست ہے؟

درستی آپ کی درج کردہ قدروں اور طریقے کے مفروضوں پر منحصر ہے۔ اعشاری حساب 50 بامعنی ہندسے استعمال کرتا ہے، مگر تخمینے، عددی طریقے اور ماخذ کا ڈیٹا کم درست ہو سکتے ہیں؛ دکھائی گئی قدروں کو راؤنڈ کرنے سے یہ حدود ختم نہیں ہوتیں۔ آزاد ذرائع کی حل شدہ مثالوں سے جانچ: 7۔ مثلاً، “⁨Course grade (default)⁩” کو ⁨Hand calculation: (92 × 20 + 85 × 30 + 78 × 50) / 100 = 8290 / 100 = 82.9⁩ سے جانچا جاتا ہے۔

### اس طریقے کا ماخذ کیا ہے؟

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

## ماخذ

- [Wolfram MathWorld: Weighted mean](https://mathworld.wolfram.com/WeightedMean.html)
- [NIST Dataplot reference manual: WEIGHTED SUM (Σ wᵢxᵢ)](https://itl.nist.gov/div898/software/dataplot/refman2/auxillar/weigsum.htm)