Statistical Analysis Calculator | Analyze Data Distribution

When outliers are present, use robust statistical measures that are less sensitive to extreme values. The median is preferred over the mean for central tendency, as a single outlier can significantly shift the mean but has minimal impact on the median. For dispersion, use the interquartile range (IQR) rather than standard deviation. Additionally, consider using trimmed means (which exclude a percentage of the highest and lowest values) or Winsorization (replacing extreme values with less extreme ones). Box plots are ideal for visualizing data with outliers as they clearly show the data's central tendency, spread, and highlight potential outliers.

To assess normality, use both visual and numerical methods. Visually, create a histogram or Q-Q plot—in a Q-Q plot, points following a straight line suggest normality. Numerically, conduct tests like Shapiro-Wilk (best for smaller samples) or Kolmogorov-Smirnov (for larger samples). A normal distribution has: (1) mean, median, and mode at approximately the same value, (2) skewness close to zero, (3) kurtosis close to three, and (4) approximately 68% of data within one standard deviation of the mean, 95% within two, and 99.7% within three. Our calculator provides these measures to help you evaluate normality easily.

Population statistics describe the entire group being studied, while sample statistics describe only a subset drawn from that population. The formulas differ slightly: population variance divides by N (total members), while sample variance divides by n-1 (degrees of freedom), making it a less biased estimator of population variance. We denote population parameters with Greek letters (μ for mean, σ for standard deviation, σ² for variance) and sample statistics with Latin letters (x̄ for mean, s for standard deviation, s² for variance). Choose "population" calculations when your data includes all members of the group; choose "sample" when your data is a subset and you want to make inferences about the larger population.