Statistics Mean Median Mode Calculator

Enter Data

Data input type

Variance method

Trim each tail (%)

Decimal places

Raw data

Use commas, spaces, semicolons, pipes, or new lines.

Frequency data

Use one value and one frequency per line. Frequencies should be positive whole numbers.

Formula Used

The calculator sorts the selected data first. Then it applies standard descriptive statistics formulas.

Measure	Formula	Meaning
Mean	`Σx / n`	Total values divided by count.
Median	`middle value`	Center value after sorting.
Mode	`highest frequency value`	Most repeated value.
Sample variance	`Σ(x - mean)² / (n - 1)`	Spread estimate for a sample.
Population variance	`Σ(x - mean)² / n`	Spread for a full population.
Standard deviation	`√variance`	Typical distance from the mean.
IQR	`Q3 - Q1`	Spread of the middle half.
Coefficient of variation	`(SD / \|mean\|) × 100`	Relative variation percentage.

How To Use This Calculator

Select raw data or frequency data.
Paste values into the correct input box.
Choose sample or population variance.
Set trim percentage if outliers should be reduced.
Choose decimal places for the output.
Press Calculate Statistics.
Review the result cards, table, and graph.
Use CSV or PDF export for reporting.

Example Data Table

This example uses exam scores. The raw values can be pasted directly into the calculator.

Data Set	Values	Expected Focus
Class A Scores	62, 68, 68, 71, 74, 78, 80, 80, 80, 86	Mode and median
Sales Calls	14, 16, 18, 18, 20, 25, 31, 34	Spread and range
Delivery Time	22, 24, 24, 25, 29, 31, 33, 40	Outlier review

Understanding Center And Spread

A statistics calculator helps you read a data set quickly. The mean shows the balanced average. The median shows the middle value. The mode shows the most repeated value. These three measures can agree. They can also tell different stories. A salary list often has a high outlier. The mean may rise. The median may stay steady. That makes comparison easier.

Why This Calculator Helps

This tool accepts raw values or grouped frequency data. It sorts the data before calculating. It also checks count, minimum, maximum, range, quartiles, variance, standard deviation, and coefficient of variation. These extra values show the shape of the data. They help you see consistency and spread. A low standard deviation means values sit close to the mean. A high value shows wider movement.

Better Review With Options

Advanced options make the results more useful. You can choose sample or population variance. Use sample variance when your data represents part of a larger group. Use population variance when your data includes every item. The trim option removes equal percentages from both tails. It helps when extreme values distort the center. Quartiles and IQR also reduce outlier pressure. They describe the middle half of the data.

Charts And Exports

The chart gives a visual check. Tall bars show common values. The box view highlights the median, quartiles, and possible extremes. Use the CSV button to save the numeric summary. Use the PDF button to create a clean report for class, work, or audits. Exported files make sharing simple.

Practical Uses

Students can test homework answers. Teachers can create quick examples. Analysts can summarize survey scores. Business users can compare sales, costs, service times, or quality checks. Always review the source data first. Remove typing errors before trusting results. Keep units consistent. Do not mix dollars, hours, and percentages in one list. Good data makes every statistic more reliable.

Reading Results Carefully

No single measure explains everything. Mean is sensitive to extreme values. Median is stable with skewed data. Mode is useful for repeated ratings or categories stored as numbers. Check all measures together. Then decide which measure matches your question best and audience.

FAQs

1. What does the mean show?

The mean shows the arithmetic average. It adds all values and divides by the number of values. It is useful for balanced data, but extreme values can pull it higher or lower.

2. What does the median show?

The median shows the center value after sorting. If the count is even, it uses the average of the two middle values. It works well with skewed data.

3. What does the mode show?

The mode shows the most repeated value. A data set can have one mode, several modes, or no repeated mode. It helps identify common outcomes.

4. Should I choose sample or population variance?

Choose sample variance when your data represents part of a larger group. Choose population variance when your data includes every value from the group being studied.

5. Why use trimmed data?

Trimmed data removes equal amounts from both ends. It can reduce the impact of extreme values. Use it only when outliers are valid but distort comparison.

6. What is standard deviation?

Standard deviation measures how far values usually sit from the mean. A small value means close grouping. A large value means wider spread.

7. What is IQR?

IQR means interquartile range. It equals Q3 minus Q1. It describes the middle half of the data and is less affected by outliers.

8. Can I export the results?

Yes. After calculation, use the CSV button for spreadsheet data. Use the PDF button for a clean printable summary with key statistics.