Weighted Mean Calculator – भारित माध्य कैलकुलेटर | GPA, Average Calculator

Weighted Mean Calculator – भारित माध्य कैलकुलेटर | GPA, Average Calculator

Weighted Mean Calculator

भारित माध्य कैलकुलेटर

Calculate weighted mean for GPA, scores, ratings with frequency support

Simple Weighted
With Frequency

Enter values and weights as comma-separated lists. Both lists must have the same number of items.

📚 Example: GPA Calculation

Grades: A(4), B+(3.5), A-(3.7), B(3)
Credits: 3, 4, 2, 3
Weighted Mean = (4×3 + 3.5×4 + 3.7×2 + 3×3) / (3+4+2+3) = 3.48

Calculation Result
Weighted Mean: 86.57
\[ \text{Weighted Mean} = \frac{\sum w \cdot x}{\sum w} \]

How to use the Weighted Mean Calculator:

  1. Select data type: Simple Weighted or With Frequency
  2. Enter your data values according to the selected type
  3. For weighted data, enter both values and their weights
  4. For frequency data, enter values and their frequencies
  5. Click Calculate to see the weighted mean with detailed calculation
  6. Download the result for future reference

When to use Weighted Mean:

  1. For calculating GPA (Grade Point Average)
  2. For course grades with different credit hours
  3. For investment portfolios with different weights
  4. For survey results with different sample sizes
  5. When different values have different importance levels

Comparison of Different Means:

Mean Type Formula Use Case
Arithmetic Mean \(\frac{\sum x}{n}\) Equal importance
Weighted Mean \(\frac{\sum w \cdot x}{\sum w}\) Different importance
Geometric Mean \(\sqrt[n]{\prod x}\) Growth rates
Harmonic Mean \(\frac{n}{\sum \frac{1}{x}}\) Rates, ratios
Simple Weighted
With Frequency

Enter values and weights as comma-separated lists. Both lists must have the same number of items.

📚 Example: GPA Calculation

Grades: A(4), B+(3.5), A-(3.7), B(3)
Credits: 3, 4, 2, 3
Weighted Mean = (4×3 + 3.5×4 + 3.7×2 + 3×3) / (3+4+2+3) = 3.48

Calculation Result
Weighted Mean: 86.57
\[ \text{Weighted Mean} = \frac{\sum w \cdot x}{\sum w} \]

How to use the Weighted Mean Calculator:

  1. Select data type: Simple Weighted or With Frequency
  2. Enter your data values according to the selected type
  3. For weighted data, enter both values and their weights
  4. For frequency data, enter values and their frequencies
  5. Click Calculate to see the weighted mean with detailed calculation
  6. Download the result for future reference

When to use Weighted Mean:

  1. For calculating GPA (Grade Point Average)
  2. For course grades with different credit hours
  3. For investment portfolios with different weights
  4. For survey results with different sample sizes
  5. When different values have different importance levels

Comparison of Different Means:

Mean Type Formula Use Case
Arithmetic Mean \(\frac{\sum x}{n}\) Equal importance
Weighted Mean \(\frac{\sum w \cdot x}{\sum w}\) Different importance
Geometric Mean \(\sqrt[n]{\prod x}\) Growth rates
Harmonic Mean \(\frac{n}{\sum \frac{1}{x}}\) Rates, ratios
Weighted Mean Calculator - भारित माध्य कैलकुलेटर: पूरी गाइड | Ganit Calculator

Weighted Mean Calculator - भारित माध्य कैलकुलेटर: पूरी गाइड

Weighted Mean (भारित माध्य) statistics का एक fundamental measure of central tendency है जो different importance levels वाले data points को handle करता है। इस comprehensive guide में हम weighted mean के सभी aspects को detailed तरीके से cover करेंगे।

Weighted Mean क्या है? (What is Weighted Mean?)

Weighted Mean या भारित माध्य एक प्रकार का average है जहां कुछ data points दूसरों की तुलना में अधिक contribute करते हैं। यह उन situations के लिए ideal है जहां different values के different levels of importance होते हैं।

\[ \text{Weighted Mean} = \frac{\sum_{i=1}^{n} w_i \cdot x_i}{\sum_{i=1}^{n} w_i} \]

Weighted Mean के प्रकार और Calculation Methods

← Scroll horizontally to view full table →
Data Type Formula उपयोग
Simple Weighted \[ \bar{x}_w = \frac{\sum w_i x_i}{\sum w_i} \] Individual values with weights
With Frequency \[ \bar{x}_w = \frac{\sum f_i x_i}{\sum f_i} \] Frequency distribution data
Probability Weights \[ \bar{x}_w = \sum p_i x_i \] Probability distributions

Calculation Methods

1. Simple Weighted Mean

जब data individual values और उनके weights के form में हो:

\[ \text{Weighted Mean} = \frac{w_1 x_1 + w_2 x_2 + \ldots + w_n x_n}{w_1 + w_2 + \ldots + w_n} \]

2. Weighted Mean with Frequency

जब values और उनकी frequencies दी गई हों (frequency ही weight का काम करती है):

\[ \text{Weighted Mean} = \frac{f_1 x_1 + f_2 x_2 + \ldots + f_n x_n}{f_1 + f_2 + \ldots + f_n} \]

3. Alternative Computational Form

Step-by-step calculation के लिए:

\[ \text{Weighted Mean} = \frac{\sum (\text{weight} \times \text{value})}{\sum \text{weights}} \]

Key Properties of Weighted Mean

Importance-Based Calculation

Weighted mean different values को उनके importance के according differently treat करता है, जबकि arithmetic mean सभी values को equally treat करता है।

Flexible Weights

Weights किसी भी positive value के हो सकते हैं - integers, decimals, percentages, आदि। Zero weight वाले values calculation में contribute नहीं करते।

Scale Dependent

Weighted mean weights के scale पर depend करता है। Relative weights matter करते हैं, absolute values नहीं।

Applications of Weighted Mean

GPA Calculation

Academic grades को credit hours के weights के साथ calculate करने के लिए perfect। Different courses के different credit hours को account करता है।

Investment Analysis

Portfolio returns calculate करने के लिए, जहां different investments के different weights होते हैं।

Survey Analysis

Survey results analyze करने के लिए जहां different groups के different sample sizes होते हैं।

Performance Evaluation

Employee performance ratings जहां different criteria के different importance levels होते हैं।

Solved Examples

Example 1: Simple Weighted Mean

Problem: एक student के different subjects के marks और उनके credit hours निम्नलिखित हैं। Weighted average निकालें।

← Scroll horizontally to view full table →
SubjectMarks (x)Credits (w)
Mathematics854
Physics903
Chemistry783
English922
Solution:
← Scroll horizontally to view full table →
Subjectxww × x
Mathematics854340
Physics903270
Chemistry783234
English922184
Total121028
\[ \sum w = 4 + 3 + 3 + 2 = 12 \]
\[ \sum w \cdot x = 340 + 270 + 234 + 184 = 1028 \]
\[ \text{Weighted Mean} = \frac{1028}{12} = 85.67 \]

Example 2: Weighted Mean with Frequency

Problem: एक class के students के marks distribution का weighted mean निकालें:

← Scroll horizontally to view full table →
Marks RangeMid Value (x)Number of Students (f)
0-20105
20-40308
40-605012
60-807010
80-100905
Solution:
← Scroll horizontally to view full table →
xff × x
10550
308240
5012600
7010700
905450
Total402040
\[ \sum f = 5 + 8 + 12 + 10 + 5 = 40 \]
\[ \sum f \cdot x = 50 + 240 + 600 + 700 + 450 = 2040 \]
\[ \text{Weighted Mean} = \frac{2040}{40} = 51 \]

Example 3: GPA Calculation

Problem: एक student के grades और credit hours निम्नलिखित हैं। GPA निकालें।

← Scroll horizontally to view full table →
CourseGrade Point (x)Credit Hours (w)
Mathematics4.03
Physics3.74
Chemistry3.33
English3.02
Solution:
← Scroll horizontally to view full table →
Coursexww × x
Mathematics4.0312.0
Physics3.7414.8
Chemistry3.339.9
English3.026.0
Total1242.7
\[ \sum w = 3 + 4 + 3 + 2 = 12 \]
\[ \sum w \cdot x = 12.0 + 14.8 + 9.9 + 6.0 = 42.7 \]
\[ \text{GPA} = \frac{42.7}{12} = 3.56 \]

Weighted Mean vs Arithmetic Mean

Aspect Weighted Mean Arithmetic Mean
Formula (∑wᵢxᵢ)/∑wᵢ (∑xᵢ)/n
Use Case Different importance levels Equal importance
Weights Explicit weights required Implicit equal weights
Sensitivity Weights affect result All values equally affect result
Application GPA, portfolio returns Average marks, temperature

Frequently Asked Questions (FAQ)

1. Weighted mean कब use करना चाहिए?

Weighted mean use करें जब:

  • Different values के different levels of importance हों
  • Frequency distribution data analyze करना हो
  • GPA या academic grades calculate करना हो
  • Investment portfolio returns calculate करना हो
  • Survey results with different sample sizes analyze करना हो

2. Weights कैसे determine करते हैं?

Weights determine करने के लिए:

  • Academic context: Credit hours, course difficulty
  • Financial context: Investment amounts, portfolio weights
  • Survey context: Sample sizes, population proportions
  • Business context: Importance factors, priority levels

3. क्या weights negative हो सकते हैं?

Theoretically, weights negative हो सकते हैं, लेकिन practical applications में weights usually positive होते हैं। Negative weights mathematical sense बना सकते हैं, लेकिन interpretation difficult हो जाती है।

Key Points to Remember

  • Weighted mean different importance levels को handle करता है
  • Weights किसी भी positive value के हो सकते हैं
  • GPA calculation weighted mean का सबसे common application है
  • Frequency distribution के लिए frequency ही weight का काम करती है
  • Weighted mean arithmetic mean से different हो सकता है
  • Relative weights matter करते हैं, absolute values नहीं

Important Note

Weighted mean calculate करते समय ensure करें कि weights positive हों और denominator (sum of weights) zero न हो। Zero denominator undefined result देगा। Practical applications में weights usually non-negative होते हैं।

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