What is the difference between mean, median, and mode?

Mean, median, and mode are three different ways to describe the 'centre' of a dataset, each with different strengths. Mean (average): add all values and divide by the count. Sensitive to outliers — one extreme value pulls the mean significantly. Best for symmetric distributions without outliers. Median (middle value): sort the data and take the middle value (or average of two middle values for even counts). Not affected by outliers. Best for skewed data or when outliers are present (e.g. income, house prices). Mode (most frequent): the value that appears most often. The only measure that works for categorical (non-numeric) data. A dataset can have no mode, one mode, or multiple modes (bimodal, multimodal). Which to use: • Symmetric data, no outliers → mean • Skewed data or outliers → median • Categorical data or finding the most common value → mode • Always report all three — together they tell more than any one alone

How do you calculate the mean (average)?

The mean is the sum of all values divided by the count: x̄ = (x₁ + x₂ + ... + xₙ) / n. For 2, 4, 4, 6, 8, 8, 8, 10: • Sum = 2+4+4+6+8+8+8+10 = 50 • Count n = 8 • Mean = 50/8 = 6.25 Types of mean: • Arithmetic mean (standard): sum/n — most common • Weighted mean: each value has a weight, used in GPA and grade calculations • Geometric mean: nth root of the product — used for growth rates and ratios • Harmonic mean: n divided by sum of reciprocals — used for rates and speeds • This calculator computes the arithmetic mean

How do you find the median of a dataset?

Sort the dataset from smallest to largest. If the count is odd, the median is the middle value. If the count is even, the median is the average of the two middle values. Odd count example — 3, 7, 7, 19, 24: • n = 5, middle position = 3rd • Median = 7 Even count example — 2, 4, 4, 6, 8, 8, 8, 10: • n = 8, middle positions = 4th and 5th • 4th value = 6, 5th value = 8 • Median = (6+8)/2 = 7 Why median matters: • House prices: if most homes cost ₹50L but one costs ₹5Cr, the mean is misleading — the median better represents the typical home • Income: median income is more representative than mean income • Any dataset with outliers: prefer the median over the mean

What is standard deviation and how is it calculated?

Standard deviation measures how spread out the data is around the mean. A small standard deviation means values are clustered near the mean; a large one means they are spread widely. Population standard deviation (σ): use when your data IS the entire population. Sample standard deviation (s): use when your data is a sample from a larger population (divides by n−1 instead of n — Bessel's correction). For 2, 4, 4, 6, 8, 8, 8, 10 (mean = 6.25): • Deviations: (2−6.25)², (4−6.25)², ... = 18.0625, 5.0625, 5.0625, 0.0625, 3.0625, 3.0625, 3.0625, 14.0625 • Sum of squared deviations = 52 • Population variance σ² = 52/8 = 6.5 • Population std dev σ = √6.5 ≈ 2.5495 • Sample variance s² = 52/7 ≈ 7.4286 • Sample std dev s ≈ 2.7261 Rule of thumb: ~68% of data falls within 1 std dev of the mean, ~95% within 2, ~99.7% within 3 (for normal distributions).

What is IQR and why is it used?

The IQR (Interquartile Range) is Q3 − Q1, where Q1 is the 25th percentile and Q3 is the 75th percentile. It measures the spread of the middle 50% of the data, making it resistant to outliers. For 2, 4, 4, 6, 8, 8, 8, 10: • Q1 (25th percentile) = 4 • Q3 (75th percentile) = 8 • IQR = 8 − 4 = 4 Why IQR matters: • Outlier detection: values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are typically considered outliers (Tukey's fence) • For this dataset: lower fence = 4 − 6 = −2, upper fence = 8 + 6 = 14 → no outliers • Box plots: the box spans from Q1 to Q3, with median marked inside • More robust than range (which is dominated by the two extreme values) • The five-number summary (min, Q1, median, Q3, max) fully describes the distribution shape

Mean Median Mode Calculator — Full Descriptive Statistics

The Mean Median Mode Calculator computes all descriptive statistics for any dataset. Enter numbers separated by commas, spaces, or new lines — the calculator instantly finds the mean (average), median (middle value), mode (most frequent value, including bimodal and no-mode cases), range, standard de...

ENTER YOUR DATA

Commas, spaces, or new lines — any format works

n = 8

MEAN

6.25

average

MEDIAN

middle

MODE

most frequent

Count (n)8

Sum50

Min2

Max10

Range8

Midrange6

Population Variance6.4375

Population Std Dev2.5372

Q1 (25th pct)4

Q3 (75th pct)8

IQR (Q3−Q1)4

Sorted data2, 4, 4, 6, 8, 8...

QUICK EXAMPLES

DOT PLOT

FIVE-NUMBER SUMMARY

Min

Median

Max

FREQUENCY TABLE

Value	Freq	Rel %	Cum %
2	1	12.5%	12.5%
4	2	25%	37.5%
6	1	12.5%	50%
8	3	37.5%	87.5%
10	1	12.5%	100%

Bold rows = mode value(s)

Created with❤️byeaglecalculator.com

HOW TO USE

1
Type or paste your numbers into the input box. Any separator works — commas, spaces, semicolons, or new lines. The calculator accepts integers, decimals, and negative numbers.
2
Mean, median, and mode appear instantly in the three black result cards. The mode card shows all modes if the data is bimodal or multimodal, or None if every value appears exactly once.
3
Toggle between Population (÷n) and Sample (÷n−1) using the buttons below the main results to switch between population and sample variance and standard deviation.
4
Check the dot plot — each data point is stacked as a dot above the number line. The blue dashed line marks the mean, red marks the median, the grey shading shows the IQR, and mode dots are black.
5
The frequency table on the right shows each unique value with its frequency, relative percentage, and cumulative percentage. Mode values are highlighted in bold.

WORKED EXAMPLE

Dataset: 2, 4, 4, 6, 8, 8, 8, 10 (n=8). Mean=50/8=6.25. Median=(6+8)/2=7 (4th and 5th values). Mode=8 (appears 3×). Range=10−2=8. Population variance=52/8=6.5. Std dev=√6.5≈2.5495. Sample variance=52/7≈7.4286. Q1=4, Q3=8, IQR=4. Five-number summary: 2, 4, 7, 8, 10.

FORMULAS

DESCRIPTIVE STATISTICS FORMULAS

NAME	FORMULA	DESCRIPTION
Mean	x̄ = Σx / n	Sum of all values divided by count
Median (odd n)	Middle value after sorting	The single central value
Median (even n)	(x_{n/2} + x_{n/2+1}) / 2	Average of two middle values
Mode	Value with highest frequency	Most common value; no mode if all unique
Population variance	σ² = Σ(x−x̄)² / n	Average squared deviation from mean
Sample variance	s² = Σ(x−x̄)² / (n−1)	Bessel corrected for sample data
Std deviation	σ = √(σ²)	Square root of variance
Range	max − min	Span from lowest to highest value
IQR	Q3 − Q1	Spread of middle 50% of data
Q1 (25th pct)	Median of lower half	25th percentile
Q3 (75th pct)	Median of upper half	75th percentile

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Last updated: April 29, 2026 · Formula verified by EagleCalculator team · Eagle-eyed accuracy for every calculation.