Mean Median and Mode Calculator

Statistical Measures:

\[ \text{Mean} = \frac{\sum x_i}{n} \] \[ \text{Median} = \text{middle value of ordered dataset} \] \[ \text{Mode} = \text{most frequent value(s)} \]

Mean:

Median:

Mode(s):

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1. What are Mean, Median and Mode?

Mean, median, and mode are three different measures of central tendency in statistics. The mean is the average value, the median is the middle value, and the mode is the most frequent value in a dataset.

2. How Does the Calculator Work?

The calculator uses standard statistical formulas:

\[ \text{Mean} = \frac{\sum x_i}{n} \] \[ \text{Median} = \text{middle value of ordered dataset} \] \[ \text{Mode} = \text{most frequent value(s)} \]

Where:

\( x_i \) — Each value in the dataset
\( n \) — Number of values in the dataset
For median: If even number of values, average of two middle numbers
For mode: Can be multiple values if they have same highest frequency

3. When to Use Each Measure

Mean: Best for normally distributed data without outliers.
Median: Better for skewed distributions or data with outliers.
Mode: Useful for categorical data or finding most common value.

4. Using the Calculator

Instructions: Enter numbers separated by commas (e.g., 5, 8, 12, 3, 8). The calculator will compute all three measures of central tendency.

5. Frequently Asked Questions (FAQ)

Q1: Which measure is most affected by outliers?
A: The mean is most affected by outliers. The median is more robust against outliers.

Q2: Can a dataset have no mode?
A: Yes, if all values appear with the same frequency (no repetition).

Q3: What if there are multiple modes?
A: The calculator will display all values that share the highest frequency.

Q4: How does the calculator handle non-numeric input?
A: Non-numeric values are automatically filtered out before calculation.

Q5: Which measure should I report?
A: It depends on your data distribution and purpose. Often reporting multiple measures gives a more complete picture.