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Median Calculator

Median Calculation:

\[ \text{Median} = \begin{cases} \text{middle value} & \text{if odd number of values} \\ \text{average of two middle values} & \text{if even number of values} \end{cases} \]

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1. What is Median?

The median is the middle value in a sorted list of numbers. It's a measure of central tendency that divides the data set into two equal halves, making it less sensitive to outliers than the mean.

2. How Does the Calculator Work?

The calculator follows these steps:

\[ \text{Median} = \begin{cases} \text{middle value} & \text{if odd number of values} \\ \text{average of two middle values} & \text{if even number of values} \end{cases} \]

Process:

  1. Sort the numbers in ascending order
  2. Count the number of values
  3. If odd count: take the middle value
  4. If even count: average the two middle values

3. Importance of Median Calculation

Details: The median provides a better central value than the mean when data contains outliers or is skewed. It's widely used in statistics, economics, and data analysis.

4. Using the Calculator

Tips: Enter numbers separated by commas (e.g., 5, 2, 7, 1, 9). The calculator will ignore any non-numeric values.

5. Frequently Asked Questions (FAQ)

Q1: When should I use median instead of mean?
A: Use median when your data has outliers or is skewed, as it's less affected by extreme values than the mean.

Q2: What's the difference between median and average?
A: Median is the middle value, while average (mean) is the sum divided by count. They can be very different in skewed distributions.

Q3: Can median be calculated for non-numeric data?
A: Yes, median can be found for ordinal data (data that can be ranked), but not for nominal data (categories without order).

Q4: How does median handle even vs odd number of values?
A: For odd counts it's the exact middle value. For even counts it's the average of the two middle values.

Q5: Is median affected by data distribution?
A: Median is less affected by distribution shape than mean, making it more robust for non-normal distributions.

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