Descriptive statistics

• How to Find a Geometric Mean When Values Are Negative
  The standard geometric mean requires positive values. Learn how to handle signed data, when shifting is misleading, and how to average negative returns.
• How to Calculate a Z-Score Without a Standard Deviation
  A z-score needs a standard deviation or equivalent information. Learn when it cannot be calculated and how to find or estimate the missing spread.
• Does Standard Deviation Change When You Add or Multiply by a Constant?
  Adding a constant leaves the standard deviation unchanged; multiplying by a scales it by |a| and the variance by a². Proof, examples and the general rule for aX + b.
• How to Find Quartiles from a Histogram (Grouped Data)
  Find Q1, the median and Q3 from a histogram using cumulative frequencies and the grouped-data interpolation formula, with a fully worked example.