Mean, Median, Mode Calculator
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What is Mean?
The arithmetic mean is the sum of all numbers divided by the count of numbers. It is calculated using the formula: \[\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}\] where $x_i$ represents each value in the dataset and $n$ is the total number of values. The mean is sensitive to extreme values and provides a measure of central tendency that takes all values into account.
What is Median?
The median is the middle value when numbers are arranged in ascending or descending order. For an odd number of values, it's the middle number. For an even number of values, it's the average of the two middle numbers. The median is less sensitive to extreme values than the mean, making it useful for skewed distributions.
What is Mode?
The mode is the value that appears most frequently in a dataset. A dataset can have no mode (if all values appear once), one mode (unimodal), two modes (bimodal), or more (multimodal). The mode is particularly useful for categorical data and can help identify the most common value in a dataset.
Examples and Applications
1. Mean: Used for calculating average scores, temperatures, or prices
2. Median: Often used for income data or house prices where extreme values might skew the mean
3. Mode: Useful for finding most common sizes, preferences, or categorical data