Coefficient of Range Calculator | परास गुणांक कैलकुलेटर

Coefficient of Range Calculator | परास गुणांक कैलकुलेटर

Coefficient of Range Calculator

परास गुणांक कैलकुलेटर

Calculate Coefficient of Range: (Max – Min) / (Max + Min)

Enter numbers separated by commas or spaces. Example: 10,15,20,25,30,35,40 or 10 15 20 25 30 35 40

Coefficient of Range Formula:
$$C_R = \frac{X_{\max} – X_{\min}}{X_{\max} + X_{\min}}$$
Where: \(C_R\) = Coefficient of Range, \(X_{\max}\) = Maximum value, \(X_{\min}\) = Minimum value

How to use the Coefficient of Range Calculator:

  1. Enter your data values separated by commas or spaces
  2. Click “Calculate Coefficient” to see the results
  3. View detailed step-by-step calculation with formulas
  4. Download the result for future reference
  5. Coefficient of Range measures relative dispersion (range relative to sum of extremes)
Calculation Result
0.6000
Coefficient of Range = (Max – Min) / (Max + Min) = 0.6000
Min
10
Max
40
Range
30
Sum of Extremes
50
Mean
25.0000
Total Numbers
7
Step by step solution:

Enter numbers separated by commas or spaces. Example: 10,15,20,25,30,35,40 or 10 15 20 25 30 35 40

Coefficient of Range Formula:
$$C_R = \frac{X_{\max} – X_{\min}}{X_{\max} + X_{\min}}$$
Where: \(C_R\) = Coefficient of Range
Calculation Result
0.6000
Coefficient of Range = (Max – Min) / (Max + Min) = 0.6000
Min
10
Max
40
Range
30
Sum of Extremes
50
Mean
25.0000
Total Numbers
7
Step by step solution:

How to use the Coefficient of Range Calculator:

  1. Enter your data values separated by commas or spaces
  2. Click “Calculate Coefficient” to see the results
  3. View detailed step-by-step calculation with formulas
  4. Download the result for future reference
  5. Coefficient of Range measures relative dispersion (range relative to sum of extremes)

Coefficient of Range Calculator: Complete Guide with Formula & Examples

📅 Last Updated: November 2024 ⏱️ Read Time: 5 minutes 🔢 Category: Statistics & Mathematics

What is Coefficient of Range?

The Coefficient of Range is a relative measure of dispersion that expresses the range of a dataset relative to the sum of its extreme values (maximum + minimum). Unlike absolute range, which can be misleading when comparing datasets of different scales, the coefficient of range provides a standardized, unit-less measure that facilitates meaningful comparisons between different datasets.

✨ Key Insight: Coefficient of Range tells you what percentage the range is of the sum of the highest and lowest values. For example, a coefficient of 0.6 means the range is 60% of the sum of extremes.

Coefficient of Range Formula

$$C_R = \frac{X_{\max} – X_{\min}}{X_{\max} + X_{\min}}$$
Where:
\(C_R\) = Coefficient of Range
\(X_{\max}\) = Maximum value in dataset
\(X_{\min}\) = Minimum value in dataset

Formula in Simple Terms:

Coefficient of Range = (Highest Value – Lowest Value) ÷ (Highest Value + Lowest Value)

This formula always produces a value between 0 and 1. A value closer to 1 indicates high dispersion relative to the scale, while a value closer to 0 indicates low dispersion.

Step-by-Step Calculation Example

Example Dataset: [10, 15, 20, 25, 30, 35, 40]

Step 1: Identify Extremes

Minimum (Xmin) = 10

Maximum (Xmax) = 40

Step 2: Calculate Range

Range = 40 – 10 = 30

Step 3: Sum of Extremes

Sum = 40 + 10 = 50

Step 4: Apply Formula

CR = 30 ÷ 50 = 0.6

Interpretation:

Coefficient of Range = 0.6 means the range is 60% of the sum of the highest and lowest values. This indicates moderate relative dispersion in the dataset.

Applications & Importance in Statistics

①

Comparing Different Datasets

When comparing test scores from two classes with different maximum marks, coefficient of range allows fair comparison of score dispersion despite different scales.

②

Quality Control

Manufacturing industries use coefficient of range to compare consistency of product dimensions across different production lines with varying specifications.

③

Financial Analysis

Analysts compare volatility of different stocks using coefficient of range, which accounts for different price levels, making comparisons meaningful.

Advantages vs. Limitations

✅ Advantages

  • Unit-less measure: Enables comparison across different units
  • Easy to calculate: Only requires extreme values
  • Simple interpretation: Value between 0 and 1
  • Not affected by sample size: Works with any dataset size
  • Quick dispersion check: Useful for preliminary data analysis

❌ Limitations

  • Ignores middle values: Only considers extremes
  • Sensitive to outliers: Extreme values distort results
  • Not for skewed distributions: May give misleading results
  • No information about shape: Doesn’t reveal distribution pattern
  • Limited use alone: Should be used with other statistical measures

Practical Examples & Case Studies

📊

Example 1: Comparing Student Performance

Scenario: Two classes took different tests with different maximum marks. Class A: Scores out of 50, Class B: Scores out of 100.

Class A: Scores = [25, 30, 35, 40, 45] → CR = (45-25)/(45+25) = 0.286

Class B: Scores = [50, 60, 70, 80, 90] → CR = (90-50)/(90+50) = 0.286

Insight: Both have same coefficient (0.286), indicating similar relative dispersion despite different scales.

🏭

Example 2: Manufacturing Quality Control

Scenario: Two machines produce bolts with target diameters of 10mm and 20mm respectively.

Machine A (10mm): Measurements = [9.8, 9.9, 10.0, 10.1, 10.2] → CR = 0.020

Machine B (20mm): Measurements = [19.6, 19.8, 20.0, 20.2, 20.4] → CR = 0.020

Insight: Both machines show same relative precision (0.020), though absolute tolerances differ.

Frequently Asked Questions (FAQ)

Q1: What does a coefficient of range of 0.5 mean?

A coefficient of 0.5 means that the range (difference between max and min) is exactly half (50%) of the sum of the maximum and minimum values. For example, if max=30 and min=10, range=20, sum=40, and 20/40=0.5.

Q2: Can coefficient of range be greater than 1?

No, coefficient of range always falls between 0 and 1 (inclusive). Since range = max-min and sum of extremes = max+min, and min≥0 for most datasets, the numerator is always less than or equal to the denominator.

Q3: When should I use coefficient of range instead of standard deviation?

Use coefficient of range for quick comparisons between datasets with different scales, especially when you only have extreme values. Use standard deviation for more precise analysis that considers all data points and distribution shape.

Q4: How is coefficient of range different from coefficient of variation?

Coefficient of range uses only extreme values and their sum, while coefficient of variation uses mean and standard deviation. Coefficient of variation is generally more robust as it considers all data points, not just extremes.

Key Takeaways

The Coefficient of Range is a valuable statistical tool for comparing relative dispersion across datasets with different scales. While it has limitations (sensitivity to outliers, ignoring middle values), its simplicity and unit-less nature make it particularly useful for preliminary analysis, quality control, and comparing datasets with different measurement units.

Remember: Always use coefficient of range alongside other statistical measures for comprehensive data analysis.

Ready to Calculate Coefficient of Range?

Use our interactive Coefficient of Range Calculator above to quickly compute this important statistical measure for your dataset. Simply enter your values and get instant results with step-by-step explanations!

📍 Bookmark this page for quick access | 📊 Perfect for students, researchers & analysts | 🔢 No installation required

Related Statistical Concepts:

Range in Statistics Coefficient of Variation Standard Deviation Measures of Dispersion Interquartile Range Relative Measures in Statistics

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