Calculate mean, median, mode, and range with our comprehensive statistical calculator. Get instant results with step-by-step explanations, perfect for homework, research, and data analysis projects.
This mean median mode range calculator provides comprehensive statistical analysis for any data set. Whether you're a student learning statistics, a teacher creating examples, or a researcher analyzing data, our calculator delivers instant results with detailed explanations for mean, median, mode, and range calculations.
Our mean median mode range calculator not only computes the values but also explains when to use each statistical measure, helping you understand data distribution patterns and make informed analytical decisions.
Sum of all values divided by the number of values
For even n: average of two middle values
Can have no mode, one mode, or multiple modes
Difference between largest and smallest values
| Measure | Best Used When | Advantages | Disadvantages |
|---|---|---|---|
| Mean | Data is normally distributed | Uses all data points, mathematically precise | Sensitive to outliers |
| Median | Data is skewed or has outliers | Not affected by extreme values | Doesn't use all information |
| Mode | Categorical data or finding most common | Shows most typical value | May not exist or be unique |
| Range | Need simple spread measure | Easy to calculate and interpret | Only uses two values |
| Distribution Type | Relationship | Best Central Measure | Example |
|---|---|---|---|
| Normal (Symmetric) | Mean = Median = Mode | Mean | Heights, test scores |
| Right Skewed | Mean > Median > Mode | Median | Income, house prices |
| Left Skewed | Mode > Median > Mean | Median | Age at death |
| Uniform | Mean ≈ Median, no clear mode | Mean or Median | Random numbers |
Unimodal: One mode (single peak in distribution)
Bimodal: Two modes (two peaks of equal height)
Multimodal: More than two modes
No Mode: All values occur with equal frequency
Dataset: 2, 10, 21, 23, 23, 38, 38
Mean Calculation:
Mean = (2 + 10 + 21 + 23 + 23 + 38 + 38) ÷ 7 = 155 ÷ 7 = 22.14
Median Calculation:
Ordered data: 2, 10, 21, [23], 23, 38, 38
Median = 23 (middle value in odd-sized dataset)
Mode Calculation:
23 and 38 both appear twice → Bimodal: 23, 38
Range Calculation:
Range = 38 - 2 = 36
| Field | Application | Primary Measure | Reason |
|---|---|---|---|
| Education | Test score analysis | Mean | Overall performance assessment |
| Real Estate | House price analysis | Median | Avoids skewing by luxury homes |
| Retail | Shoe size inventory | Mode | Most common size to stock |
| Quality Control | Product measurements | Mean & Range | Central value and variation |
| Healthcare | Patient age distribution | Median | Typical patient age |
Original Dataset: 2, 10, 21, 23, 23, 38, 38
With Outlier: 2, 10, 21, 23, 23, 38, 38, 1000
Compare Measures: Look at all three measures together to understand data distribution shape and characteristics.
Consider Context: The "best" measure depends on your specific purpose and the nature of your data.
Check for Outliers: Identify and decide how to handle extreme values based on your analysis goals.
Communicate Clearly: Always specify which measure you're reporting and why it's appropriate for your situation.
Average Always Represents Typical: In skewed distributions, the mean may not represent a typical value.
More Decimal Places = More Accuracy: Precision in calculation doesn't guarantee accuracy if the wrong measure is used.
Mode Must Exist: Some datasets have no mode if all values occur equally often.
Range Shows Complete Spread: Range only uses two values and doesn't show how data is distributed between them.
Example Dataset: 4, 7, 9, 10, 15, 15, 18
Mean Calculation:
Step 1: Add all values: 4 + 7 + 9 + 10 + 15 + 15 + 18 = 78
Step 2: Divide by count: 78 ÷ 7 = 11.14
Mean = 11.14
Median Calculation:
Step 1: Sort data: 4, 7, 9, 10, 15, 15, 18
Step 2: Find middle position: Position 4 (7 values)
Median = 10
Mode Calculation:
Step 1: Count frequencies: 4(1), 7(1), 9(1), 10(1), 15(2), 18(1)
Step 2: Find highest frequency: 15 appears twice
Mode = 15
Range Calculation:
Step 1: Find maximum: 18
Step 2: Find minimum: 4
Step 3: Subtract: 18 - 4 = 14
Range = 14
Academic Research: Analyze survey data, test scores, experimental results, and research findings with comprehensive statistical measures.
Business Analytics: Evaluate sales data, customer metrics, performance indicators, and market research using mean, median, mode, and range analysis.
Quality Control: Monitor manufacturing processes, product measurements, and quality metrics with statistical analysis tools.
Educational Projects: Complete homework assignments, understand statistical concepts, and prepare for exams with step-by-step solutions.