Mean, Median, Mode & Range Calculator with Steps

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Formula at a glance

Mean Median Mode Calculator: Mean — x̄ = Σx / n. Example: 15 values → Mean (average): 22 — How the Mean Median Mode Calculator works: Mean — x̄ = Σx / n

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📘 About the Mean, Median, Mode & Range Calculator

The mean, median and mode are the three common averages. The mean adds everything and divides by the count; the median is the middle value when sorted; the mode is the most frequent value. Together with the range (largest − smallest) they summarise a data set.

Paste your numbers. The calculator sorts them, finds the mean, median (averaging the two middle values for an even count), every mode (or none), the range, quartiles and the standard deviation, and charts the frequency of each value.

🧮 Formula

Mean

x̄ = Σx / n

Median

middle value of the sorted data (average of the two middle values if n is even)

Range

max − min

✏️ Worked examples

15 values

You enter
Data	3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29

You get
Mean (average)	22
Median (middle value)	23
Mode (most frequent)	23 (appears 4 times)
Range	53 (3 to 56)
Count	15
Sum	330
Quartiles Q1 · Q3	12 · 29
Sorted data	3, 5, 7, 12, 13, 14, 20, 23, 23, 23, 23, 29, 39, 40, 56
Standard deviation (sample)	14.506156

Mean 22, median 23.

Exam marks

You enter
Data	72, 85, 90, 65, 85, 78, 92, 85, 70, 88

You get
Mean (average)	81
Median (middle value)	85
Mode (most frequent)	85 (appears 3 times)
Range	27 (65 to 92)
Count	10
Sum	810
Quartiles Q1 · Q3	72 · 88
Sorted data	65, 70, 72, 78, 85, 85, 85, 88, 90, 92
Standard deviation (sample)	9.2255683

Mean 81, median 85, mode 85 (appears 3 times).

🧭 How to use this calculator

What you enter

DataSeparate numbers with commas, spaces or new lines.

What you get

Mean (average)
Median (middle value)
Mode (most frequent)
Range
Count
Sum
Quartiles Q1 · Q3
Sorted data
Standard deviation (sample)

❓ Frequently asked questions

What is the difference between mean and median?

The mean uses every value and is pulled by extremes; the median is the middle value and is not. For incomes or house prices the median is a better typical value.

Can there be more than one mode?

Yes — two modes is bimodal, more is multimodal. If every value appears once, there is no mode.

How do I find the median of an even number of values?

Sort the data and average the two middle values: for 2, 4, 6, 8 the median is (4 + 6)/2 = 5.

📊 Mean, Median, Mode & Range Calculator