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Median Calculator

Median Formula:

\[ \text{Median} = \begin{cases} \text{middle value} & \text{if odd number of values} \\ \frac{\text{value at } n/2 + \text{value at } (n/2 + 1)}{2} & \text{if even number of values} \end{cases} \]

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1. What is Median?

The median is the middle value in a sorted list of numbers. Unlike the mean, it's not affected by extremely large or small values, making it a robust measure of central tendency.

2. How to Calculate Median

The median is calculated differently depending on whether you have an odd or even number of values:

\[ \text{Median} = \begin{cases} \text{middle value} & \text{if odd number of values} \\ \frac{\text{value at } n/2 + \text{value at } (n/2 + 1)}{2} & \text{if even number of values} \end{cases} \]

Steps:

  1. Sort the numbers in ascending order
  2. Count the number of values (n)
  3. If odd: Median is the middle value
  4. If even: Median is average of two middle values

3. When to Use Median

Details: Median is preferred over mean when:

4. Using the Calculator

Tips: Enter numbers separated by commas. The calculator will:

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between median and mean?
A: Mean is the average (sum divided by count), while median is the middle value. Median is less affected by outliers.

Q2: Can median be calculated for non-numeric data?
A: Yes, median can be found for ordinal data (data that can be ranked).

Q3: How does median handle even vs odd counts?
A: For odd counts, it's the exact middle. For even, it's the average of two middle values.

Q4: When is median better than mean?
A: For skewed distributions or when outliers are present, median gives a better "typical" value.

Q5: Can median be outside the range of data?
A: No, median is always one of the values (odd count) or between two values (even count).

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