Statistics Calculator
Complete descriptive statistics: mean, median, mode, standard deviation, skewness, kurtosis, quartiles, z-scores, outlier detection, frequency table, and box plot.
6
Mean
3.4254
Std Dev (σ)
15
Count (n)
Enter Your Data
Sample Datasets
Mean
6
Median
5
3.4254
Pop SD (σ)
3.5456
Sample SD (s)
15
Count (n)
90
Sum
13
Range
1
Outliers (IQR)
Complete Descriptive Statistics
15
Count (n)
90
Sum
6
Mean (x̄)
5
Median
4, 5
Mode
3.4254
Pop SD (σ)
3.5456
Sample SD (s)
11.7333
Pop Variance (σ²)
12.5714
Sample Variance
2
Min
15
Max
13
Range
4
Q1 (25th pctile)
5
Q2 (Median)
8
Q3 (75th pctile)
4
IQR (Q3-Q1)
1.1744
Skewness
0.8391
Excess Kurtosis
59.09%
Coeff of Variation
2.6667
MAD (Mean Abs Dev)
6.9089
RMS (Root Mean Sq)
5.1526
Geometric Mean
4.4293
Harmonic Mean
-2
Lower Fence
14
Upper Fence
716
Sum of Squares
1
Outliers (IQR)
Box & Whisker Plot
Histogram
Outlier Detection
IQR Method
Lower fence: Q1 − 1.5×IQR = -2
Upper fence: Q3 + 1.5×IQR = 14
Z-Score Method
|z| > 2 (mild): 1 value
|z| > 3 (extreme): 0 values
Frequency Distribution Table
| Value | Freq | Rel Freq | Cum Freq | Bar |
|---|---|---|---|---|
| 2 | 2 | 13.3% | 13.3% | |
| 3 | 1 | 6.7% | 20% | |
| 4 | 3 | 20% | 40% | |
| 5 | 3 | 20% | 60% | |
| 6 | 1 | 6.7% | 66.7% | |
| 7 | 1 | 6.7% | 73.3% | |
| 8 | 1 | 6.7% | 80% | |
| 9 | 1 | 6.7% | 86.7% | |
| 11 | 1 | 6.7% | 93.3% | |
| 15 | 1 | 6.7% | 100% | |
| Total | 15 | 100% | 100% |
Sorted Data & Z-Scores
| Value | Deviation (x−mean) | Z-Score | IQR Outlier? |
|---|---|---|---|
| 2 | -4 | -1.1677 | No |
| 2 | -4 | -1.1677 | No |
| 3 | -3 | -0.8758 | No |
| 4 | -2 | -0.5839 | No |
| 4 | -2 | -0.5839 | No |
| 4 | -2 | -0.5839 | No |
| 5 | -1 | -0.2919 | No |
| 5 | -1 | -0.2919 | No |
| 5 | -1 | -0.2919 | No |
| 6 | 0 | 0 | No |
| 7 | 1 | 0.2919 | No |
| 8 | 2 | 0.5839 | No |
| 9 | 3 | 0.8758 | No |
| 11 | 5 | 1.4597 | No |
| 15 | 9 | 2.6274 | Yes |
Comprehensive Descriptive Statistics
Descriptive statistics summarize and describe the main features of a data set. Unlike inferential statistics, they don't try to predict anything beyond your data or test a hypothesis — they simply describe what's actually there. This calculator is built to be the every-stat-at-once tool: paste a list of numbers and get the full picture instead of hunting down each measure separately. If you only need one quick answer, our narrower mean, median, mode & range calculator or standard deviation calculator will get you there faster.
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Central Tendency
Mean, median, and mode each describe a data set's “center” differently. The mean is sensitive to extreme values, the median resists them, and the mode reveals the single most common value — this calculator also adds geometric and harmonic mean for ratio- and rate-based data.
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Dispersion & Spread
Range, variance, standard deviation, IQR, mean absolute deviation, and coefficient of variation all measure how spread out your data is, in different units and with different sensitivities to extreme values.
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Shape & Skewness
Skewness measures asymmetry — which tail of the distribution stretches further — while excess kurtosis measures how heavy or light the tails are compared to a normal, bell-shaped distribution.
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Outlier Detection
Values that sit unusually far from the rest of the data are flagged two ways: the 1.5×IQR fence method (the box-plot standard) and a z-score check for values more than 2 or 3 standard deviations from the mean.
Key Statistical Measures
Central tendency: Mean, Median, Mode, Geometric Mean, Harmonic Mean | Spread: SD, Variance, Range, IQR, MAD, CV | Shape: Skewness, Excess Kurtosis | Position: Q1, Q2 (Median), Q3, Percentiles, Z-scores | 5-number summary: Min, Q1, Median, Q3, Max | Box plot outliers (IQR): below Q1 − 1.5×IQR or above Q3 + 1.5×IQR— FAQ