Mean Median Mode Range Calculator — Free Online Tool

How to Use the Mean Median Mode Range Calculator

1. Enter your numbers: Type or paste your dataset into the text area. Separate values with commas, spaces, or new lines. The calculator automatically detects valid numbers and displays the count below the input field. You can paste data directly from spreadsheets.
2. Read the four primary measures: The top section displays the arithmetic mean (average), median (middle value), mode (most frequent value), and range (max minus min) in large, easy-to-read cards. Each card includes a brief definition for quick reference.
3. Check additional means: Below the primary results, find the geometric mean and harmonic mean. The geometric mean is best for growth rates and ratios, while the harmonic mean is ideal for averaging rates and speeds.
4. Review summary statistics: The bottom section shows the count, sum, minimum, and maximum values, along with the sorted dataset for verification.

All calculations update in real time. The calculator handles any dataset size and displays results to four decimal places for precision. If all values are unique, the mode shows "None" since no value appears more frequently than others.

Mean, Median, Mode, and Range Formulas

Variables Explained

• x₁, x₂, ..., xₙ: The individual data values in your dataset. Each value is a single observation or measurement.
• n: The total number of values in the dataset. This is the count of observations used in the calculations.
• Median: The middle value after sorting all values in ascending order. For even-sized datasets, it is the average of the two middle values.
• Mode: The value that appears most frequently. A dataset may have zero, one, or multiple modes.

Step-by-Step Example

Find the mean, median, mode, and range for: 3, 7, 7, 12, 15, 18, 18, 18, 24

1. Count the values: n = 9
2. Calculate the sum: 3 + 7 + 7 + 12 + 15 + 18 + 18 + 18 + 24 = 122
3. Arithmetic Mean: 122 / 9 = 13.556
4. Median: Data is already sorted. The 5th value (middle of 9) = 15
5. Mode: 18 appears 3 times (most frequent) = 18
6. Range: 24 - 3 = 21

Notice that mean (13.556) is less than median (15), which is less than mode (18). This pattern suggests a slightly left-skewed distribution where a few lower values pull the mean downward.

Practical Examples

Example 1: Emma's Budget Analysis

Emma tracks her monthly grocery spending for a year: $320, $285, $310, $295, $340, $310, $275, $310, $365, $290, $310, $330. She wants to understand her typical spending pattern to create a realistic budget for next year.

• Mean: $311.67 (her average monthly spending)
• Median: $310 (the middle spending amount)
• Mode: $310 (appearing 4 times, her most common spending level)
• Range: $365 - $275 = $90

All three central tendency measures converge around $310, giving Emma confidence that this is her typical monthly grocery cost. The range of $90 shows moderate variability. She sets her monthly budget at $320 (slightly above the mean) to accommodate occasional higher-spending months while maintaining discipline.

Example 2: James's Running Performance

James is training for a 5K race and records his practice times (in minutes): 28.5, 27.3, 26.8, 29.1, 26.5, 25.9, 26.8, 27.0, 26.2, 26.8. He wants to know his typical pace and consistency.

• Mean: 27.09 minutes (his average time)
• Median: 26.8 minutes (the middle time)
• Mode: 26.8 minutes (appearing 3 times)
• Range: 29.1 - 25.9 = 3.2 minutes

The convergence of median and mode at 26.8 minutes suggests this is James's natural pace. The mean is slightly higher due to one slower run (29.1 minutes, possibly a bad day). His range of 3.2 minutes shows fairly consistent performance. For his race goal, targeting 27 minutes is realistic based on his median time.

Example 3: Company Salary Analysis

A small company has 10 employees with annual salaries (in thousands): $42, $45, $48, $50, $52, $55, $58, $62, $75, $180. The HR team needs to report a representative salary figure.

• Mean: $66,700 (inflated by the CEO's $180K salary)
• Median: $53,500 (between $52K and $55K)
• Mode: None (all values unique)
• Range: $180K - $42K = $138K

This example perfectly illustrates why median is preferred for salary data. The mean of $66,700 exceeds what 80% of employees actually earn because the CEO's $180K salary pulls it upward. The median of $53,500 better represents the typical employee's compensation. When presenting to job candidates, the median gives a more honest picture. For more comprehensive statistical analysis, try our statistics calculator.

Comparison of Mean Types

Tips and Complete Guide

Quick Decision Guide for Central Tendency

Start by asking: Is your data roughly symmetric? If yes, the mean is your best choice because it uses all data points and has desirable mathematical properties. If your data is skewed or has outliers, the median is more representative. If you need to find the most common category or value, use the mode. When in doubt, report all three measures and let the reader understand the full picture.

The Relationship Between Mean and Median

The difference between mean and median is a quick indicator of skewness. If the mean is substantially greater than the median, your data is right-skewed (a long tail of high values). If the mean is substantially less than the median, your data is left-skewed. When they are approximately equal, the distribution is roughly symmetric. This comparison is faster than calculating the formal skewness coefficient and gives you an immediate sense of your data's shape.

Handling Special Cases

Some datasets present unique challenges. Bimodal distributions (two peaks) suggest your data might come from two distinct populations that should be analyzed separately. Datasets with many ties can have multiple modes, making interpretation difficult. Very small datasets (fewer than 5 values) should be interpreted cautiously, as the statistics may not be representative. For datasets with zeros or negative values, the geometric mean cannot be calculated. Our calculator handles all these cases gracefully and clearly indicates when a measure cannot be computed.

Common Mistakes to Avoid

• Using the mean for skewed data without context: Always check for skewness before relying solely on the mean. If you report only the mean salary at a company where the CEO earns 10 times the median employee, you are giving a misleading picture.
• Confusing "no mode" with "mode is zero": If zero is the most frequent value, zero is the mode. If no value appears more than once, there is no mode. These are fundamentally different situations.
• Interpreting range without context: A range of 50 means something very different for test scores (0-100 scale) versus temperatures (in a moderate climate). Always consider the range relative to the scale of measurement.
• Averaging percentages directly: You cannot simply average percentage changes or growth rates using the arithmetic mean. Use the geometric mean for compounding rates to get accurate results.
• Forgetting that the geometric mean requires all positive values: If your dataset includes zero or negative numbers, the geometric mean is undefined. Check your data before applying this measure.

Frequently Asked Questions