Math & Engineering
Mean, Median, Mode & Range Calculator
Calculate the mean (average), median (middle value), mode (most frequent value), and range (spread) of a dataset.
Enter numbers to see statistical results
Related to Mean, Median, Mode & Range Calculator
This calculator performs comprehensive statistical analysis on a set of numbers by computing four fundamental measures of central tendency and spread: mean, median, mode, and range. Each measure provides unique insights into your data distribution:
Mean (Average)
The mean is calculated by summing all numbers and dividing by the count of numbers. It represents the arithmetic average and is sensitive to all values in the dataset, including outliers. For example, in the dataset [1, 2, 3, 4, 5], the mean is (1+2+3+4+5)/5 = 3.
Median (Middle Value)
The median is found by arranging numbers in ascending order and selecting the middle value. For an even count of numbers, it's the average of the two middle values. The median is less sensitive to outliers than the mean. For example, in [1, 2, 3, 4, 5], the median is 3.
Mode (Most Frequent)
The mode identifies the most frequently occurring number(s) in the dataset. A dataset can have no mode (if all numbers appear once), one mode (unimodal), or multiple modes (multimodal). For example, in [1, 2, 2, 3, 4], the mode is 2.
Range (Spread)
The range measures the spread of the data by calculating the difference between the largest and smallest values. It provides insight into data dispersion but is sensitive to outliers. For example, in [1, 2, 3, 4, 5], the range is 5 - 1 = 4.
Understanding these statistical measures together provides a comprehensive view of your data distribution. Here's how to interpret the results effectively:
Central Tendency Analysis
Compare the mean and median to understand data skewness. If they're similar, your data is likely symmetrically distributed. If they differ significantly, your data may be skewed. The mode helps identify the most common value(s), which is particularly useful for categorical or discrete data.
Data Spread Assessment
The range provides a simple measure of variability. A larger range indicates more spread-out data, while a smaller range suggests the data points are closer together. However, remember that the range is sensitive to outliers and should be considered alongside other measures.
1. When should I use mean vs. median?
Use the mean when your data is symmetrically distributed and outliers aren't a concern. Use the median when your data is skewed or contains outliers, as it's less sensitive to extreme values. For example, median income is often more representative than mean income due to income inequality.
2. What does it mean if there's no mode?
If there's no mode, it means all values in your dataset appear exactly once (uniform frequency). This is common in continuous data or small datasets. Multiple modes indicate several values that appear with equal highest frequency.
3. How does the range help in data analysis?
The range helps identify the spread of your data and potential outliers. A large range might indicate significant variability or the presence of outliers. However, since it only uses two values (minimum and maximum), it should be used alongside other measures like standard deviation for a complete analysis.
4. Can these measures be used for any type of data?
These measures are most appropriate for numerical data (continuous or discrete). The mean requires numerical values for calculation. The median needs ordered data. The mode can be used with any data type, including categorical data. The range only makes sense for numerical data with a meaningful order.
5. What is the scientific source for this calculator?
This calculator implements statistical measures based on established mathematical principles from fundamental statistics. The formulas and methodologies are derived from core statistical theory as documented in standard statistical references such as "Statistical Methods" by G.W. Snedecor and W.G. Cochran, and "Introduction to the Practice of Statistics" by Moore, McCabe, and Craig. The calculations follow the standard definitions used in descriptive statistics: arithmetic mean (sum divided by count), median (middle value after sorting), mode (most frequent value), and range (difference between maximum and minimum values).