Median Calculator
Enter your values to find the median - the middle value in a sorted dataset.
Result
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Batch Import - You can paste multiple values separated by spaces. They will be automatically distributed across the input fields.
When to use median - The median is particularly useful when your data contains outliers, as it is less affected by extreme values than the mean.
Median Formula
To calculate the median manually, follow these steps:
For the dataset [3, 7, 9, 12, 15], the median is 9 (the middle value). For [3, 7, 9, 12, 15, 18], the median is (9 + 12) / 2 = 10.5 (average of the two middle values).
Sort all values from smallest to largest. If there's an odd number of values, the median is the middle value. If there's an even number of values, the median is the average of the two middle values.
What is Median?
The median is a measure of central tendency that represents the middle value in a sorted dataset.
Unlike the arithmetic mean (average), the median is not affected by extreme values or outliers. This makes it a more robust measure of central tendency when your data contains unusually high or low values that could skew the average.
The median is widely used in statistics, economics, and data analysis. Common applications include reporting median household income (which better represents typical earnings than the mean), real estate prices, and any dataset where outliers could distort the average.
When to Use Median
The median is the preferred measure of central tendency in many real-world scenarios:
- Income and Salaries: Median salary better reflects typical income than mean, which can be skewed by extremely high earners.
- Real Estate Prices: Median home price shows typical pricing without distortion from luxury properties.
- Ratings and Reviews: Median rating is more resistant to fake reviews (1★ or 5★ spam).
Frequently Asked Questions About Median
- How do you calculate the median with an even number of values?
- With an even number of values, the median is the average of the two middle values. For example, for [2, 4, 6, 8], the middle values are 4 and 6, so the median is (4+6)/2 = 5.
- Can the median be different from the average?
- Yes, and they often differ. In symmetric distributions (like normal), the mean and median are equal. But in asymmetric distributions or data with outliers, they can differ significantly.
- Why are salaries often reported as median rather than average?
- Because a few very high salaries (executives, athletes) would raise the average and give a distorted picture. The median shows what 50% of the population earns: half more, half less.
- Is the median always one of the values in the data?
- Not always. With an odd number of values, the median is one of the values. With an even number, the median is the average of the two middle values, which may be a number that doesn't exist in the data.
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