Mean, Median & Mode Calculator

About Mean, Median & Mode Calculator

Enter a dataset and instantly get the mean, median, mode, range, minimum, maximum, and sum. Values are shown sorted with median position highlighted, and a frequency table with bar chart shows the distribution at a glance.

What Are Mean, Median, and Mode?

These three measures of central tendency each answer the question "what is a typical value?" in a different way:

Measure	Definition	Best Used When
Mean	Sum of all values divided by the count	Data is symmetric with no extreme outliers
Median	The middle value when data is sorted	Data is skewed or has outliers
Mode	The most frequently occurring value	Data is categorical or you want the "most common"

How to Calculate Each Measure

Mean:

Mean = (sum of all values) / (number of values)

Dataset: 4, 7, 2, 9, 7, 3, 8

• Sum = 4 + 7 + 2 + 9 + 7 + 3 + 8 = 40
• Count = 7
• Mean = 40 / 7 = 5.714

Median:

1. Sort the data: 2, 3, 4, 7, 7, 8, 9
2. Count = 7 (odd), so the median is the middle value
3. Middle position = (7 + 1) / 2 = 4th value
4. Median = 7

For even-count datasets: the median is the average of the two middle values.

• Dataset: 3, 5, 7, 9 (4 values)
• Two middle values: 5 and 7
• Median = (5 + 7) / 2 = 6

Mode:

• Dataset: 2, 3, 4, 7, 7, 8, 9
• 7 appears twice, all others appear once
• Mode = 7

When Mean and Median Disagree

The relationship between mean and median tells you about the shape of the data:

Relationship	Shape	Example
Mean ≈ Median	Symmetric	Heights of adults: mean and median both around 170 cm
Mean > Median	Right-skewed (positive skew)	Income: a few high earners pull the mean up
Mean < Median	Left-skewed (negative skew)	Retirement age: most retire at 65, a few retire very early

Classic example: In a room of 10 people earning £30K each, the mean and median income are both £30K. If one person gets a raise to £1 million, the mean jumps to £127K but the median stays at £30K. This is why median income is more informative than mean income for understanding "typical" earnings.

Types of Mode

Type	Meaning	Example Dataset
No mode	All values appear equally often	1, 2, 3, 4, 5
Unimodal	One mode	1, 2, 2, 3, 4
Bimodal	Two modes	1, 1, 2, 3, 3
Multimodal	Three or more modes	1, 1, 2, 2, 3, 3

Additional Summary Statistics

Beyond the three central tendency measures, the calculator also shows:

Statistic	Definition	For dataset 2, 3, 4, 7, 7, 8, 9
Range	Maximum - Minimum	9 - 2 = 7
Sum	Total of all values	40
Count	Number of values	7
Minimum	Smallest value	2
Maximum	Largest value	9

Which Average to Report?

Context	Best Measure	Why
Test scores (symmetric)	Mean	Uses all data, most precise when distribution is normal
House prices	Median	Extreme values (mansions) skew the mean
Salary data	Median	A few high earners distort the mean
Shoe sizes sold	Mode	You want the most popular size to stock
Survey ratings (1-5)	Mode or Median	Ordinal data - mean of 3.7 stars is harder to interpret
Scientific measurements	Mean	Random errors cancel out; mean is the best estimate

Weighted Mean

When some values count more than others, use a weighted mean:

Weighted mean = Σ(value × weight) / Σ(weights)

Example: A course grade with homework (30%), midterm (30%), and final (40%):

• Homework: 85, Midterm: 78, Final: 92
• Weighted mean = (85 × 0.3) + (78 × 0.3) + (92 × 0.4) = 25.5 + 23.4 + 36.8 = 85.7
• The unweighted mean would be (85 + 78 + 92) / 3 = 85.0 - slightly different

For standard deviation and variance calculations that build on the mean, the standard deviation calculator takes the analysis further. For a simpler tool focused just on averages, the average calculator handles weighted and unweighted means.

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