Mean Median Mode Calculator with Steps
Calculate mean, median, and mode with complete step-by-step explanations. Learn central tendency measures and data analysis. Free calculator.
Quick Answer
Mean = sum of values ÷ count. Median = middle value (or average of two middle). Mode = most frequent value. Mean sensitive to outliers, median robust, mode shows popularity. Essential for understanding data distribution and central tendency.
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Calculate Mean Median Mode with Steps
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Calculate With Full ToolWhat are Mean, Median, and Mode?
Mean, median, and mode are the three main measures of central tendency in statistics. They describe the center or typical value of a dataset, each providing different insights into data distribution and helping identify patterns and outliers.
How They Work Together
These measures complement each other in data analysis. When all three are similar, the data is likely normally distributed. Differences between them can indicate skewness, outliers, or multiple peaks in the data distribution.
Choosing the Right Measure
Mean works best for symmetric data without outliers. Median is ideal for skewed data or when outliers are present. Mode is useful for categorical data or identifying the most common values in a dataset.
Mean Median Mode Formulas
Mean: μ = Σx / n
Median: Middle value when sorted
Mode: Most frequent value
Mean Formula: μ = Σx / n (sum of all values ÷ number of values)
Median (Odd n): Middle value after sorting
Median (Even n): Average of two middle values
Mode: Value(s) that appear most frequently
Range: Maximum value - Minimum value
Step-by-Step Example
Example: Calculate for data [10, 15, 12, 18, 20, 14, 16]
Step 1: Sort data: [10, 12, 14, 15, 16, 18, 20]
Step 2: Calculate mean: (10+12+14+15+16+18+20) ÷ 7 = 105 ÷ 7 = 15
Step 3: Find median: Middle value = 15 (4th position)
Step 4: Find mode: No repeated values (no mode)
Step 5: Calculate range: 20 - 10 = 10
Example: Even number of values [2, 4, 6, 8, 10, 12]
Step 1: Calculate mean: (2+4+6+8+10+12) ÷ 6 = 42 ÷ 6 = 7
Step 2: Find median: (6 + 8) ÷ 2 = 7 (average of middle values)
Step 3: Find mode: No repeated values (no mode)
Step 4: Interpret: Mean = Median = 7 (symmetric distribution)
These examples show the calculation process for both odd and even numbers of values. When mean equals median, the data is typically symmetric around the center.
Who Should Use This Calculator?
Students
Learn statistics and complete assignments
Data Analysts
Analyze data distributions and patterns
Researchers
Summarize experimental data and results
Business Analysts
Analyze sales data and performance metrics
Frequently Asked Questions
When should I use mean vs median?
Use mean for symmetric data without outliers. Use median when data is skewed or contains extreme values, as it's not affected by outliers and better represents the typical value in such cases.
Can a dataset have multiple modes?
Yes, a dataset can be multimodal with two or more values appearing equally frequently. Bimodal distributions have two modes, which often indicate two distinct groups or patterns in the data.
What does it mean when mean > median?
When mean is greater than median, the data is positively skewed (right-skewed). This means there are outliers or a tail of high values pulling the mean upward, while the median better represents the typical value.
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