Statistics Calculator
FAQ
Descriptive statistics and interpretation
Difference between sample and population variance?
Sample variance divides by (n-1) (Bessel's correction) when data is a sample of a larger population. Population variance divides by n when data represents the entire population.
What do skewness and kurtosis indicate?
Skewness > 0: right-tailed; < 0: left-tailed; = 0: symmetric. Excess kurtosis > 0: leptokurtic (peakier than normal); < 0: platykurtic (flatter); = 0: mesokurtic (like normal).
What is IQR and what is it for?
IQR (Interquartile Range) = Q3 - Q1 measures the spread of the middle 50% of data and is robust to outliers. Used for outlier detection: values outside [Q1 - 1.5·IQR, Q3 + 1.5·IQR] are flagged.
When to use geometric or harmonic mean?
Geometric mean fits growth rates and compound returns (e.g. annual ROI). Harmonic mean suits ratios and rates (e.g. price per unit or km/h on equal-length trips).
When do I use the sample variance?
When the data is a sample of a wider population: you divide by the number of observations minus one, the Bessel correction. When the data is the whole population you divide by the full count.
What do skewness and kurtosis tell me?
Skewness says which way the distribution stretches: positive to the right, negative to the left. Kurtosis says whether it is more peaked or flatter than the normal curve.
What is the interquartile range for?
It measures how spread out the middle half of the data is, and extreme values cannot throw it off. It is used to spot outliers, which sit more than one and a half times that range beyond the quartiles.