Calculate mean, median, and mode with detailed step-by-step solutions. Enter your numbers and get comprehensive analysis of central tendency measures. Perfect for students, teachers, and data analysts. No Signup Required.
Calculate measures of central tendency with detailed explanations
Enter your numbers above to calculate measures of central tendency
• Mean: The arithmetic average of all values
• Median: The middle value when data is ordered
• Mode: The most frequently occurring value(s)
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Discover the power of mean, median, and mode in statistical analysis with these fascinating insights!
The concept of "average" dates back to ancient civilizations, with early forms used in Babylonian mathematics around 2000 BCE!
The word "median" comes from the Latin "medius," meaning middle - perfectly describing its function!
Mode gets its name from the French "mode," meaning fashionable - it's the most "popular" value!
In perfectly symmetrical data, the mean, median, and mode are all exactly equal!
Mean is sensitive to outliers - one extreme value can dramatically change the average
Median is robust against outliers - it only cares about the middle position
Mode is the only measure that can be used with categorical data like colors or names
A dataset can have no mode, one mode (unimodal), or multiple modes (multimodal)!
Grade analysis, test score interpretation, class performance evaluation, and academic benchmarking
Sales performance, customer satisfaction ratings, employee productivity, and market research analysis
Patient vital signs, treatment effectiveness, diagnostic measurements, and population health studies
Property price analysis, market trends, neighborhood comparisons, and investment decisions
Player performance statistics, team scoring averages, game analysis, and talent evaluation
Survey data analysis, experimental results, demographic studies, and scientific measurements
• Data is normally distributed
• No significant outliers
• You need mathematical precision
• Comparing different groups
• Planning or forecasting
• Data has outliers
• Distribution is skewed
• You want typical value
• Income or price data
• Ordinal data analysis
• Categorical data
• Most popular choice
• Survey responses
• Product preferences
• Discrete data patterns
Scores: 85, 90, 78, 92, 88, 95, 82, 89, 91, 87
Mean = 87.7 (overall class performance), Median = 88.5 (middle performer), Mode = None (all unique)
Prices: $200k, $250k, $300k, $320k, $1.2M
Mean = $454k (skewed by mansion), Median = $300k (better typical value)
Sizes: S, M, M, L, M, XL, M, L, M
Mode = M (most popular size to stock), Mean/Median don't apply to categories
Ratings: 5, 4, 5, 3, 5, 4, 5, 2, 5, 5
Mean = 4.3, Median = 5, Mode = 5 (most common rating)
x̄ = mean (x-bar)
Σx = sum of all values
n = number of values
Sort data first
Odd n: middle value
Even n: average of two middle values
Count frequencies
Find maximum frequency
Return all values with max frequency
Mean, median, and mode are the three main measures of central tendency. Mean is the arithmetic average (sum of all values divided by count). Median is the middle value when data is arranged in order. Mode is the value(s) that appear most frequently. These measures help describe the center or typical value of a dataset.
Use mean for normally distributed data without outliers - it's the most common measure. Use median when data has outliers or is skewed, as it's less affected by extreme values. Use mode for categorical data or when you want to know the most common value. For example, median is better for income data (due to high earners), while mode is useful for survey responses or product ratings.
Enter numbers separated by spaces, commas, semicolons, or new lines. For example: '5, 10, 15, 20' or '5 10 15 20' or each number on a separate line. The calculator automatically detects the format and processes your data. You can also copy and paste data directly from spreadsheets like Excel or Google Sheets.
If all values appear with the same frequency, there is no mode - the calculator will display 'None'. If two or more values tie for the highest frequency, your data is multimodal and the calculator will show all mode values. For example, in the dataset [1,2,2,3,3,4], both 2 and 3 are modes (bimodal distribution).
For an odd number of values, the median is the middle value after sorting. For an even number of values, the median is the average of the two middle values. For example: [1,2,3,4,5] has median 3, while [1,2,3,4] has median 2.5 (average of 2 and 3). The calculator shows the detailed process for both cases.
Absolutely! This calculator is perfect for analyzing test scores, grades, and academic performance. You can calculate the average score (mean), find the middle performance level (median), and identify the most common score (mode). This helps teachers and students understand class performance and grade distribution patterns.
Mean and average are the same thing - both refer to the arithmetic mean calculated by adding all values and dividing by the count. The term 'average' is more commonly used in everyday language, while 'mean' is the technical statistical term. There are other types of averages (like geometric mean), but when people say 'average,' they usually mean the arithmetic mean.
Outliers significantly affect the mean, pulling it toward extreme values. The median is resistant to outliers since it only depends on the middle value(s). The mode is unaffected by outliers unless the outlier itself becomes the most frequent value. For data with outliers, median often provides a better representation of the 'typical' value than mean.