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Generate the first N prime numbers or list all primes inside a custom range. Includes prime count, largest prime, total sum, average prime gap, and twin-prime pair count for quick number-theory exploration.
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📊
Median Calculator
Find the median of any dataset instantly, with quartiles (Q1, Q3), IQR, five-number summary, interactive box plot, outlier detection using Tukey fences, percentile table, MAD, and Pearson skewness. Robust central tendency analysis for statistics, data science, and research.
10 values · even count → average of two middle values
Median (10 values — even count)
80.5
(78 + 83) ÷ 2
Min
65
Q1 (25th)
73
Median
80.5
Q3 (75th)
87
Max
91
Box Plot (Five-Number Summary)
65Q1MQ391
Spread & Distribution
IQR
14
Range
26
Std Dev
8.59302
MAD
8
Mean
79.6
Sum
796
Lower Fence
52
Upper Fence
108
Skewness: -0.314208 — Symmetric
Percentile Values
P10
68.6
P25
73
P50
80.5
P75
87
P90
90.1
▶Sorted values (10)
65697276788384889091
Median value
What Is the Median?
The median is the middle value of a dataset when sorted in order. It is the most widely used robust measure of central tendency because, unlike the arithmetic mean, it is not distorted by extreme values or outliers. Exactly 50% of values fall at or below the median — making it equivalent to the 50th percentile.
📍
True Middle
50% of values are below, 50% above. Unaffected by how extreme the largest or smallest values are.
🛡️
Outlier-Resistant
The median of 1, 2, 3, 4, 1000 is 3 — not 202. Perfect for skewed data like incomes or house prices.
📦
Quartile Foundation
Q1 (25th) and Q3 (75th) percentiles extend the median into a five-number summary and IQR.
Mean vs. Median rule of thumb: Use the mean for symmetric data. Use the median for skewed distributions or when outliers are present. When mean > median, the data is right-skewed; when mean < median, it is left-skewed.
How to Use This Calculator
- 1Enter your dataPaste or type numbers separated by commas, spaces, or newlines. Or click a sample dataset to load example values instantly.
- 2Read the medianThe large result card shows the median and explains whether it is the exact middle value (odd count) or the average of two middle values (even count).
- 3Review the box plotThe interactive box plot visualises the five-number summary: min, Q1, median, Q3, max. Outlier dots appear in orange beyond the Tukey fences.
- 4Check IQR and outliersThe Spread & Distribution panel shows IQR, range, standard deviation, MAD, fence thresholds, and any detected outliers.
- 5Explore percentilesToggle Custom Percentiles to enter any percentile you need (e.g. P10 and P90 for decile analysis). The default table shows P10, P25, P50, P75, P90.
How the Calculations Work
📍
Median
Sort → middle value (odd n) OR (n/2 + n/2+1) / 2 (even n)
Always sort first. For odd n take index ⌊n/2⌋. For even n average positions n/2 and n/2+1 (1-indexed).
📦
Quartiles (Q1 & Q3)
Linear interpolation at p=25 and p=75
Uses the inclusive interpolation method (same as Excel PERCENTILE.INC): value = sorted[i] + frac × (sorted[i+1]−sorted[i]) where i = (p/100)×(n−1).
📏
IQR & Tukey Fences
IQR = Q3 − Q1 · Fences: Q1 ± 1.5×IQR, Q1 ± 3×IQR
Values outside Q1 − 1.5×IQR or Q3 + 1.5×IQR are mild outliers. Beyond 3×IQR are extreme outliers.
📐
MAD (Median Absolute Deviation)
MAD = median(|xᵢ − median(x)|)
Compute each value's absolute distance from the median, then take the median of those distances. Highly robust to outliers.
↗️
Skewness (Pearson's 2nd)
Skew = 3 × (mean − median) / σ
A quick non-parametric skewness estimate. Near 0 = symmetric; positive = right-skewed; negative = left-skewed.
📊
Percentiles
P_p = sorted[i] + frac × (sorted[i+1] − sorted[i])
where i = ⌊(p/100)×(n−1)⌋ and frac = fractional part. This is the standard linear interpolation used by numpy, R, and Excel.
Worked Examples
① Odd Count — Test Scores
Dataset: 65, 69, 72, 76, 78, 83, 84, 88, 90, 91 (already sorted above — 10 values)
Wait — this is even. Let's use 7 values: 3, 7, 1, 15, 9, 4, 12
Step 1 — Sort: 1, 3, 4, 7, 9, 12, 15
Step 2 — n = 7 (odd) → position ⌊7/2⌋ + 1 = position 4
Median = 7
② Even Count — Test Scores
Dataset: 65, 69, 72, 76, 78, 83, 84, 88, 90, 91 (10 values)
Sorted: 65, 69, 72, 76, 78, 83, 84, 88, 90, 91
n = 10 (even) → positions 5 and 6
Median = (78 + 83) / 2 = 80.5
③ Outlier Detection — House Prices (£000s)
Dataset: 290, 298, 300, 305, 315, 320, 325, 335, 410, 1250
Median = (315 + 320) / 2 = 317.5
Q1 = 300.75 Q3 = 368.75 IQR = 68
Upper fence = 368.75 + 1.5 × 68 = 470.75
1250 is an outlier → Mean = 514.8 (distorted!) but Median = 317.5 (reliable)
④ Skewness — Income Data
When median income is $45,000 but mean income is $72,000, the distribution is right-skewed (a small number of high earners pulls the mean up).
Mean Income
$72,000
inflated by high earners
Median Income
$45,000
typical worker's income
Frequently Asked Questions
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Explore This Tool in Context
Median Calculator is part of the Math & Statistics Calculators collection. If you want a broader view of similar workflows, open the Math & Statistics Calculators category page or browse all QuickTools categories.
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