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Mean, median, mode & range

Mean, Median, Mode, Range Calculator

This calculator computes mean (arithmetic average), median, mode, range, and geometric mean from one list using xΛ‰=βˆ‘x/n\bar{x}=\sum x/n and R=maxβ‘βˆ’min⁑R=\max-\min. Enter comma-, space-, or newline-separated numbers or load examples; optional Logic Trace shows sorting, summation, frequency map, and range steps. Mean precision 0–5 decimal places (default 2). Descriptive only; not inference.

By Jeff Beem

Updated

Data entry

Enter numbers separated by commas, spaces, or new lines. Use the quick-fill options or load an example to get started.

Invalid entries are ignored.

Result

Enter numbers to see statistics

Use commas, spaces, or new lines. Try "Random sample" or "Load example" to get started.

How to use this calculator

Enter numbers in Dataset (commas, spaces, or new lines) or use Random sample / Load example. Set Mean precision (decimal places) (default 2). The Result pane lists mean, median, mode, range, and related fields; toggle Show Logic Trace for four step cards and the sorted bar. Copy to clipboard exports the summary when data is present.

Reading your statistics result

The Result pane updates as you type. Use Load example buttons for fixed data sets; Random sample generates 10–20 values. Match Mean precision before copying results.

Example: Test scores β†’ mean 83.20, mode 85

Click Load example: Test scores. Result: mean (average) 83.20, median 85, mode 85, range 20.00, count 10, sum 832. Logic Trace Step 2 shows Ξ£x = 832, n = 10, xΜ„ = 83.20.

Example: Heights (even n) β†’ median 170.50, no mode

Click Load example: Heights (eight values). Mean 169.88, median 170.50 from (169 + 172) Γ· 2, mode No Mode, range 22.00 (180 βˆ’ 158). Sorted bar shows the bracketed middle pair.

Mean, median, mode, range calculator

This page computes descriptive statistics from one list and shows optional step-by-step Logic Trace work. Dataset starts empty until you enter or load values.

What this calculator does

The widget parses comma-, space-, or newline-separated numbers, then reports mean (arithmetic average), median (middle value), mode (most frequent value(s)), range (max βˆ’ min), geometric mean (when all values are positive), plus sum, count, min, and max. Optional Logic Trace walks through sorting, xΛ‰=βˆ‘x/n\bar{x}=\sum x/n, a frequency map for mode, and range. Copy to clipboard exports the Result summary.
  • Limits:
    Descriptive statistics only; no inference, confidence intervals, or weighted means. Geometric mean shows N/A if any value ≀ 0.

How the math works

Mean divides the sum by the count. Median uses the center of the sorted list; even n averages the two middle entries. Mode requires a frequency above one; ties return all modes. Range uses only the sorted minimum and maximum.
xΛ‰=βˆ‘xin\bar{x}=\frac{\sum x_i}{n}
Check with Load example: Heights (n = 8): median (169 + 172)/2 = 170.5, no mode, R = 22. Mean for that set is about 169.88 at two decimal places.

Limits

Does not compute standard deviation, quartiles, or regression. Random sample uses integers 1–100 only. Educational reference; verify critical work independently.

Mean Median Mode Range Calculator FAQ

What does Random sample produce?

Fills Dataset with 10–20 random integers from 1 to 100. Statistics and Logic Trace update immediately; use it to explore mean versus median with skewed draws.

How is the median calculated when n is even?

After sorting, the median averages the two middle values; the sorted bar brackets that pair. With an odd count, the median is the single center value after sort.

What if no value repeats (no mode)?

The Result pane shows No Mode. Step 3 in Logic Trace reports when no value appears more than once; bimodal sets list every value tied at the highest frequency.

What do Mean precision and Logic Trace control?

Mean precision (decimal places) rounds the mean, range, sum, min, max, and geometric mean (0–5; default 2). Median stays an integer when it is whole. Uncheck Show Logic Trace to hide the four step cards; statistics still update live.

How do I enter data?

Paste or type numbers in Dataset; commas, spaces, or new lines work. Invalid tokens are skipped. Buttons: Random sample (10–20 integers 1–100), Load example: Test scores, Load example: Heights, Clear.

When should I report median instead of mean?

Use the median when outliers would pull the mean away from a typical value (incomes, housing prices). This page prints both from the same list; compare them in the Result pane after sorting in Logic Trace Step 1.

What is range on this calculator?

Range is largest minus smallest after sorting: R=maxβ‘βˆ’min⁑R=\max-\min. The sorted bar highlights the minimum and maximum values (rose ring on max).

How is this different from the statistics or standard deviation calculators?

This tool focuses on mean, median, mode, range, and geometric mean with a four-step Logic Trace. The statistics calculator adds quartiles and a fuller profile; the standard deviation calculator centers on variance and spread beyond min/max.

Sources & citations

References used for the calculation method and definitions. Links open in a new tab when available.

[1]
NIST/SEMATECH e-Handbook of Statistical Methods β€” Measures of Location

Definitions of mean, median, and mode used in descriptive statistics.

Mathematical Reference Note

Calculation Logic: This tool uses standard mathematical algorithms. While we strive for accuracy, errors in logic or user input can result in incorrect data.

Verification: Results should be cross-checked if used for important academic, professional, or personal calculations.

Standard Terms: This tool is provided free of charge and as-is. CalcRegistry provides no warranty regarding the accuracy or fitness of these results for your specific needs.

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