Median Calculator
Calculate the median and quartiles of your dataset
How to Use
- Enter your data values separated by spaces, commas, or semicolons
- Ensure you have at least 2 numerical values
- Click calculate to find the median and quartiles
- Review the complete statistical analysis including IQR
- Use the results to understand data distribution and identify outliers
What is Median?
The median is the middle value in a dataset when the values are arranged in order. It's a measure of central tendency that divides the data into two equal halves - 50% of values fall below the median and 50% fall above it.
For datasets with an odd number of values, the median is the middle value. For even-numbered datasets, it's the average of the two middle values. This makes the median particularly useful for understanding typical values in skewed distributions.
Understanding Quartiles
Quartiles divide your data into four equal parts:
- Q1 (First Quartile): 25th percentile - 25% of data falls below this value
- Q2 (Second Quartile): 50th percentile - This is the median
- Q3 (Third Quartile): 75th percentile - 75% of data falls below this value
Quartiles help understand the spread and distribution of your data, making them essential for statistical analysis and data visualization.
Interquartile Range (IQR)
The Interquartile Range (IQR) is the difference between the third and first quartiles (IQR = Q3 - Q1). It represents the middle 50% of your data and is a robust measure of variability.
The IQR is particularly useful because it's not affected by extreme outliers, making it more reliable than the range for understanding data spread.
Outlier Detection Using IQR
The IQR method is a standard way to identify outliers:
- Lower fence: Q1 - 1.5 × IQR
- Upper fence: Q3 + 1.5 × IQR
- Values below the lower fence or above the upper fence are considered outliers
This method helps identify unusual values that might represent measurement errors, special cases, or genuinely rare events in your data.
When to Use Median vs. Mean
Choose between median and mean based on your data characteristics:
| Situation | Use Median | Use Mean |
|---|---|---|
| Skewed data | ✓ | ✗ |
| Outliers present | ✓ | ✗ |
| Symmetric data | Either | ✓ |
| Need mathematical properties | ✗ | ✓ |
| Income/wealth data | ✓ | ✗ |
| Temperature averages | Either | ✓ |
Real-World Applications
Median calculations are widely used in various fields:
- Economics: Median income and wealth distribution
- Real estate: Median home prices
- Education: Median test scores
- Healthcare: Median patient recovery times
- Finance: Median returns on investments
- Demographics: Median age and population statistics
Frequently Asked Questions
- What's the difference between median and mean?
- The median is the middle value when data is sorted, while the mean is the average of all values. The median is less affected by extreme outliers, making it better for skewed data like income distributions.
- How do you calculate quartiles?
- Q1 is the median of the lower half of data, Q3 is the median of the upper half. Different methods exist for calculating quartiles, but this calculator uses the inclusive method that includes the median in both halves for even datasets.
- What makes a good sample size for median calculation?
- For meaningful results, aim for at least 10-15 data points. While you can calculate a median with just 2 values, larger samples provide more reliable statistical insights.
- How do I interpret the interquartile range?
- The IQR represents the spread of the middle 50% of your data. A small IQR indicates consistent values, while a large IQR shows high variability. It's more robust than range because it ignores outliers.
- Can the median be the same as the mean?
- Yes, in perfectly symmetric distributions (like normal distributions), the median equals the mean. This indicates balanced data without skew.
- How are outliers identified using the IQR method?
- Values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR are considered outliers. This method identifies the most extreme 0.7% of values in a normal distribution.
- Should I remove outliers from my data?
- Not automatically. First investigate whether outliers are data errors, special cases, or legitimate extreme values. The decision depends on your analysis goals and the context of your data.
- Can negative numbers have a median?
- Absolutely. The median calculation works with any real numbers, positive or negative. The median simply represents the middle value regardless of sign.