Statistics Calculator

Calculate mean, median, mode, standard deviation, variance, quartiles, and more. Complete statistical analysis with visualizations.

Summary Statistics

Mean

27.0000

n = 10

Median26.5000
Std Dev10.7806
Min / Max12 / 45

Enter Data

10 valid numbers entered

Central Tendency

Mean

27.0000

Median

26.5000

Mode

12, 15, 18...

Geometric Mean

24.9720

Spread & Variability

Std Deviation

10.7806

Variance

116.2222

Range

33.0000

CV

39.93%

Standard Error

3.4091

Sum

270

Quartiles & Distribution

Min

12

Q1 (25%)

19.00

Q2 (Median)

26.50

Q3 (75%)

33.75

Max

45

Interquartile Range (IQR)

IQR = Q3 - Q1 = 33.75 - 19.00 = 14.75

Distribution Shape

Skewness

0.2887

Approximately symmetric

Kurtosis (Excess)

-0.8447

Platykurtic (light tails)

Distribution Histogram

Sorted Data

12, 15, 18, 22, 25, 28, 30, 35, 40, 45

Statistical Formulas

Mean

x̄ = Σx / n

Variance (sample)

s² = Σ(x - x̄)² / (n-1)

Standard Deviation

s = √(variance)

Standard Error

SE = s / √n

?How Do You Calculate Basic Statistics?

For a data set, calculate: Mean (average) = sum of values / count. Median = middle value when sorted. Mode = most frequent value. Standard deviation measures spread from mean. Variance = standard deviation squared. For data [2,4,4,4,5,5,7,9]: Mean = 5, Median = 4.5, Mode = 4, Standard Deviation = 2.14, Variance = 4.57.

What is Descriptive Statistics?

A statistics calculator performs comprehensive statistical analysis including measures of central tendency (mean, median, mode), measures of spread (variance, standard deviation, range), and data distribution analysis.

Key Facts About Statistics

  • Mean (arithmetic average) = sum of all values / number of values
  • Median = middle value in sorted data (average of two middle if even count)
  • Mode = most frequently occurring value (can have multiple modes)
  • Standard deviation measures spread/dispersion from the mean
  • Variance = standard deviation squared
  • Range = maximum value - minimum value
  • Outliers affect mean more than median
  • Normal distribution: 68% of data within 1 SD, 95% within 2 SD, 99.7% within 3 SD

Quick Answer

For a data set, calculate: Mean (average) = sum of values / count. Median = middle value when sorted. Mode = most frequent value. Standard deviation measures spread from mean. Variance = standard deviation squared. For data [2,4,4,4,5,5,7,9]: Mean = 5, Median = 4.5, Mode = 4, Standard Deviation = 2.14, Variance = 4.57.

Frequently Asked Questions

Mean is the average (sum/count). Median is the middle value when sorted. Mode is the most frequent value. Use mean for symmetric data, median for skewed data (resistant to outliers), and mode for categorical data.
Standard deviation measures how spread out data is from the mean. Low SD means data clusters near the mean; high SD means data is spread out. It's the square root of variance and uses the same units as the original data.
Quartiles divide sorted data into four equal parts. Q1 (25th percentile), Q2 (median), Q3 (75th percentile). IQR (Interquartile Range) = Q3 - Q1, representing the middle 50% of data. Used to identify outliers.
Skewness measures asymmetry: positive = right tail longer, negative = left tail longer, zero = symmetric. Kurtosis measures tail heaviness: positive = heavy tails, negative = light tails. Normal distribution has skewness 0, kurtosis 0.
Coefficient of Variation (CV) is the standard deviation expressed as a percentage of the mean: CV = (SD/mean) × 100%. It allows comparison of variability between datasets with different units or vastly different means.

Last updated: 2025-01-15