Mean Median Mode Range Calculator (MMMR)
माध्य, माध्यिका, बहुलक, परास कैलकुलेटर
Calculate Central Tendency Measures with Step-by-Step Solutions
Enter values and frequencies as comma-separated lists. Both lists must have the same number of items.
Enter class intervals as ‘start-end’ and frequencies as comma-separated lists. Both lists must have the same number of items.
| Statistical Measure | Value |
|---|
How to use the Statistics Calculator:
सांख्यिकी कैलकुलेटर का उपयोग कैसे करें:
- Select the type of series: Individual, Discrete, or Continuous
- Enter your data values according to the selected series type
- Click Calculate to see all statistical measures
- View detailed table, step-by-step solution and chart
- Download the result for future reference
Enter values and frequencies as comma-separated lists. Both lists must have the same number of items.
Enter class intervals as ‘start-end’ and frequencies as comma-separated lists. Both lists must have the same number of items.
How to use the Statistics Calculator:
सांख्यिकी कैलकुलेटर का उपयोग कैसे करें:
- Select the type of series: Individual, Discrete, or Continuous
- Enter your data values according to the selected series type
- Click Calculate to see all statistical measures
- View detailed table, step-by-step solution and chart
- Download the result for future reference
| Statistical Measure | Value |
|---|
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Mean Median Mode Range Calculator - Complete Guide
What are Mean, Median, Mode and Range?
Mean, Median, Mode and Range are the four fundamental statistical measures used to describe data sets. They help us understand the central tendency and dispersion of data, making them essential for data analysis in mathematics, statistics, research, and everyday life.
माध्य, माध्यिका, बहुलक और परास चार मूलभूत सांख्यिकीय माप हैं जिनका उपयोग डेटा सेटों का वर्णन करने के लिए किया जाता है। ये हमें डेटा की केंद्रीय प्रवृत्ति और फैलाव को समझने में मदद करते हैं, जिससे ये गणित, सांख्यिकी, शोध और रोजमर्रा की जिंदगी में डेटा विश्लेषण के लिए आवश्यक हो जाते हैं।
1. Mean (Average) - माध्य
Formula - सूत्र
The mean, commonly known as the average, is calculated by adding all values in a data set and dividing by the number of values. It's the most commonly used measure of central tendency but can be affected by outliers.
Data: 10, 15, 20, 25, 30
Calculation: (10 + 15 + 20 + 25 + 30) / 5 = 100 / 5 = 20
Mean: 20
2. Median - माध्यिका
Formula - सूत्र
The median is the middle value in a sorted data set. For even number of values, it's the average of two middle values. Median is less affected by outliers compared to mean.
Odd data points: 10, 15, 20, 25, 30
Median: 20 (middle value)
Even data points: 10, 15, 20, 25, 30, 35
Median: (20 + 25) / 2 = 22.5
3. Mode - बहुलक
Formula - सूत्र
The mode is the value that appears most frequently in a data set. A data set can have one mode (unimodal), two modes (bimodal), or multiple modes (multimodal).
Data: 10, 15, 20, 20, 25, 30
Mode: 20 (appears twice)
Bimodal data: 10, 15, 15, 20, 20, 25
Modes: 15 and 20
4. Range - परास
Formula - सूत्र
Range measures the spread or dispersion of data. It shows how spread out the values are in a data set. While easy to calculate, it's sensitive to outliers.
Data: 10, 15, 20, 25, 30
Calculation: 30 (largest) - 10 (smallest) = 20
Range: 20
Comparison Table
| Measure | Definition | When to Use | Advantages | Limitations |
|---|---|---|---|---|
| Mean | Average of all values | Normally distributed data | Uses all data points | Affected by outliers |
| Median | Middle value | Skewed data, outliers present | Robust to outliers | Ignores extreme values |
| Mode | Most frequent value | Categorical data, finding peaks | Works for non-numeric data | May not exist or be unique |
| Range | Difference between max and min | Quick spread assessment | Easy to calculate | Sensitive to outliers |
Real-World Applications
Use Case: Calculating average marks, median scores, most frequent grades, and score ranges
Example: Class test scores analysis to identify performance patterns
Use Case: Sales analysis, price ranges, customer age groups, income distribution
Example: Finding average sales per day and identifying best-selling products
Use Case: Patient age analysis, treatment effectiveness, symptom frequency
Example: Calculating average recovery time and most common symptoms
Frequently Asked Questions
A: Use mean for normally distributed data without outliers. Use median when data has outliers or is skewed, as median is less affected by extreme values.
A: Yes, a data set can be bimodal (two modes) or multimodal (multiple modes) if multiple values have the same highest frequency.
A: For even number of values, median is calculated as the average of the two middle values when the data is sorted in ascending order.
A: Range only considers the extreme values and ignores the distribution of all other values, making it sensitive to outliers.
Step-by-Step Calculation Guide
Data Set: 12, 15, 18, 22, 22, 25, 28, 30, 35
| Step 1: Sort Data | 12, 15, 18, 22, 22, 25, 28, 30, 35 |
| Step 2: Calculate Mean | (12+15+18+22+22+25+28+30+35)/9 = 207/9 = 23 |
| Step 3: Find Median | Middle value (5th position) = 22 |
| Step 4: Identify Mode | Most frequent value = 22 (appears twice) |
| Step 5: Calculate Range | 35 (max) - 12 (min) = 23 |
Results: Mean = 23, Median = 22, Mode = 22, Range = 23
Master Statistical Calculations
Understanding Mean, Median, Mode and Range is essential for data analysis. These fundamental statistical measures provide valuable insights into data distribution and central tendency.
माध्य, माध्यिका, बहुलक और परास को समझना डेटा विश्लेषण के लिए आवश्यक है। ये मूलभूत सांख्यिकीय माप डेटा वितरण और केंद्रीय प्रवृत्ति में मूल्यवान अंतर्दृष्टि प्रदान करते हैं।