Mean Range Median Mode Calculator

Statistical Formulas:

\[ \text{Mean} = \frac{\sum x}{n} \] \[ \text{Range} = \max(x) - \min(x) \] \[ \text{Median} = \text{middle value of sorted data} \] \[ \text{Mode} = \text{most frequent value} \]

Count (n):

Mean:

Range:

Median:

Mode:

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1. What Are Mean, Range, Median, and Mode?

Mean, range, median, and mode are fundamental statistical measures used to describe and analyze data sets. They provide different perspectives on the central tendency and dispersion of numerical values.

2. How Does the Calculator Work?

The calculator uses the following formulas:

\[ \text{Mean} = \frac{\sum x}{n} \] \[ \text{Range} = \max(x) - \min(x) \] \[ \text{Median} = \text{middle value of sorted data} \] \[ \text{Mode} = \text{most frequent value} \]

Where:

\( x \) — Individual values in the dataset
\( n \) — Number of values in the dataset
\( \sum x \) — Sum of all values
\( \max(x) \) — Maximum value in the dataset
\( \min(x) \) — Minimum value in the dataset

3. Importance of Statistical Measures

Details: These measures help summarize and understand data distributions. Mean provides average value, range shows data spread, median indicates central value, and mode identifies most common value.

4. Using the Calculator

Tips: Enter numerical values separated by commas. The calculator will compute all four statistical measures from your input data.

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 it's less affected by extreme values than the mean.

Q2: Can a dataset have more than one mode?
A: Yes, a dataset can be bimodal (two modes) or multimodal (multiple modes) if multiple values appear with the same highest frequency.

Q3: What does a large range indicate?
A: A large range indicates that the values in the dataset are spread out over a wide interval.

Q4: Are these measures affected by outliers?
A: Mean and range are sensitive to outliers, while median and mode are more resistant to extreme values.

Q5: What if all values are unique?
A: If all values appear only once, the dataset has no mode (or all values are considered modes).