Statistics Calculator
Mean, median, mode, standard deviation, variance, quartiles, IQR and skewness
bar_chartEnter Data Set
Enter numbers separated by commas, spaces or new lines
Statistical Formulas
Mean (μ): Sum of all values ÷ Count
Median: Middle value of sorted data (average of two middle values if even count)
Mode: Most frequently occurring value(s)
Population Variance (σ²): Σ(x−μ)² / N
Sample Variance (s²): Σ(x−μ)² / (N−1)
Standard Deviation: √Variance
IQR: Q3 − Q1 (middle 50% of data)
Skewness: Measures asymmetry; 0 = symmetric, positive = right-skewed
Mean (Average)
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Std Deviation (Pop.)
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σ (population)
Count (N)
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Sum
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Median
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Mode
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Minimum
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Maximum
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Range
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Max − Min
Skewness
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Q1 (25th Percentile)
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Q3 (75th Percentile)
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IQR
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Q3 − Q1
Std Dev (Sample)
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s (sample)
Variance (Pop.)
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σ²
Variance (Sample)
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s²
Frequency Distribution
Sorted Data
What is a Statistics Calculator?
A statistics calculator computes descriptive statistics for a dataset — measures of central tendency (mean, median, mode) and measures of spread (range, variance, standard deviation, IQR). These metrics summarize the distribution and variability of data in research, business analytics, and academics.
Standard deviation tells you how spread out data points are from the mean. A low SD means data clusters closely; a high SD means wide spread. Quartiles and IQR help identify outliers and understand the middle 50% of your data.
lightbulb Example Calculation
Scenario: Dr. Meena Pillai, research scientist at IISc Bengaluru — analysing patient response times (seconds) from a clinical trial: 4, 8, 6, 5, 3, 7, 9, 2, 6, 5. Needs mean, median, mode, and standard deviation for her paper
1Mean = (4+8+6+5+3+7+9+2+6+5) / 10 = 55/10 = 5.5
2Sorted: 2,3,4,5,5,6,6,7,8,9 → Median = (5+6)/2 = 5.5
3Mode = 5 and 6 | Std Dev ≈ 2.06 | Range = 7
✓ Mean 5.5 | Median 5.5 | Mode 5,6 | SD 2.06
help_outlineHow to Use the Statistics Calculator
- Enter your dataset in the text area — numbers separated by commas, spaces, or new lines (e.g., "4, 7, 13, 2, 8, 4, 11"). You can paste directly from Excel.
- Click "Calculate Statistics" — all measures are computed simultaneously: mean, median, mode, standard deviation (population and sample), variance, quartiles, IQR, range, and skewness.
- Review the Frequency Distribution chart to visualise how often each value appears in the dataset and identify clusters.
- Check the Sorted Data section at the bottom to see the ascending order — useful for manually verifying median and quartile positions.
- Use the Clear button to reset the input and start a new analysis with a fresh dataset.
Benefits
- 12+ statistics computed in one click — no need to calculate mean, SD, and quartiles separately
- Both population and sample variance/SD shown — critical distinction for academic and research use
- Frequency distribution chart visualises data spread without needing external tools like Excel
- Accepts any dataset size — paste hundreds of values from a spreadsheet for bulk analysis
- Skewness shows data asymmetry — detect right-skewed or left-skewed distributions instantly
Key Terms
- Mean (μ)
- Arithmetic average = Sum / Count; sensitive to outliers; the "center of gravity" of the dataset
- Median
- Middle value of sorted data; not affected by outliers; preferred for skewed distributions like income or housing prices
- Mode
- Most frequently occurring value; a dataset can have no mode, one mode, or multiple modes (bimodal)
- Standard Deviation (σ)
- √Variance; measures spread from the mean; low SD = clustered tightly, high SD = widely dispersed
- IQR
- Interquartile Range = Q3 − Q1; range of the middle 50% of data; used to detect outliers (values beyond Q1 − 1.5×IQR or Q3 + 1.5×IQR)
quizFrequently Asked Questions
What is the difference between population and sample standard deviation?
Population SD (σ) uses N as denominator: σ = √(Σ(x−μ)² / N). Sample SD (s) uses N−1 (Bessel's correction): s = √(Σ(x−μ)² / (N−1)). Use population SD when your dataset IS the entire population (e.g., all exam scores of a specific class). Use sample SD when your data is a sample from a larger population (e.g., a survey of 100 employees from a company of 5,000) — the N−1 correction removes the downward bias introduced by estimating population mean from the sample mean.
When should I use median instead of mean?
Use median when data is skewed or contains extreme outliers. Classic example: if 9 employees earn ₹30,000/month and 1 earns ₹10,00,000, the mean salary is ₹1,27,000 — misleadingly high and unrepresentative of the typical employee. The median (₹30,000) is far more meaningful. Income data, property prices, hospital billing, and startup valuations are standard cases where median better captures the "typical" value. Use mean when data is normally distributed with no extreme outliers.
What does skewness indicate about my data distribution?
Skewness measures asymmetry: skewness = 0 means a perfectly symmetric distribution (bell curve). Positive skewness (right-skewed): long tail to the right — most values cluster at the low end with a few very high values (e.g., wealth distribution, claim amounts in insurance). Negative skewness (left-skewed): long tail to the left — most values are high with a few very low (e.g., age at retirement). In finance, positive skewness in returns is desirable (occasional large gains), while negative skewness is undesirable (occasional large losses).
How is IQR used to detect outliers?
Tukey's standard outlier detection method: Lower Fence = Q1 − 1.5 × IQR; Upper Fence = Q3 + 1.5 × IQR. Values below the lower fence or above the upper fence are flagged as outliers. Example: data with Q1=10, Q3=20, IQR=10 → Lower fence=−5, Upper fence=35. A data point of 50 would be flagged as an outlier. This IQR-based method is more robust to extreme values than mean ± 2SD because it uses percentile-based boundaries instead of the mean, which itself can be distorted by outliers.
What does a high standard deviation mean for my data?
A high SD means data points are spread far from the mean — indicating high variability or inconsistency. Example: two student batches with the same mean score of 70%: Batch A SD=5 (most scored 65–75%, consistent teaching); Batch B SD=20 (scores ranged from 30–100%, highly inconsistent outcomes). In finance, high SD of returns = high investment risk (volatility). In manufacturing, high SD = poor process control and high defect rates. In medicine, high SD of patient measurements may indicate a heterogeneous treatment response.