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Median Calculator

Median Formula:

\[ \text{Median} = \begin{cases} \frac{(n+1)}{2}\text{th term} & \text{if } n \text{ is odd} \\ \frac{\frac{n}{2}\text{th term} + (\frac{n}{2}+1)\text{th term}}{2} & \text{if } n \text{ is even} \end{cases} \]

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1. What is Median?

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

2. How Does the Calculator Work?

The calculator uses the median formula:

\[ \text{Median} = \begin{cases} \frac{(n+1)}{2}\text{th term} & \text{if } n \text{ is odd} \\ \frac{\frac{n}{2}\text{th term} + (\frac{n}{2}+1)\text{th term}}{2} & \text{if } n \text{ is even} \end{cases} \]

Where:

Explanation: For an odd number of values, the median is the middle value. For an even number of values, it's the average of the two middle values.

3. Importance of Median Calculation

Details: The median is particularly useful when dealing with skewed distributions or datasets containing outliers, as it provides a better representation of the "typical" value than the mean in these cases.

4. Using the Calculator

Tips: Enter numeric values separated by commas. The calculator will sort the values and calculate the median. Example: "5, 2, 8, 1, 9" or "3.5, 2.1, 7.8, 4.2".

5. Frequently Asked Questions (FAQ)

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

Q2: Does the calculator handle decimal values?
A: Yes, the calculator works with both integer and decimal values.

Q3: What if I have duplicate values in my dataset?
A: Duplicate values are handled normally and included in the sorted dataset before calculating the median.

Q4: How many values can I input?
A: There's no strict limit, but extremely large datasets may take longer to process.

Q5: Can I use this for both population and sample data?
A: Yes, the median calculation is the same for both population and sample data.

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