Question

how do ik how high the standard deviation is between 2 box and whisker plots

Answer 1

Short answer: you generally cannot get the exact standard deviation from two boxplots alone unless you have the raw data or make distributional assumptions. But you can estimate relative spread from the boxplot and, if you assume approximate normality, convert the IQR to an approximate SD.

What a boxplot shows
- Box = IQR = Q3 − Q1 (middle 50% of the data).
- Line in the box = median.
- Whiskers = range of non-outlier values (commonly min/max within 1.5·IQR).
- Outliers plotted individually.

How to estimate SD from a boxplot
- If the data are approximately normal, IQR ≈ 1.349·σ, so:
σ ≈ IQR / 1.349
- Example: if one box has IQR = 6 and another IQR = 9,
σ1 ≈ 6 / 1.349 ≈ 4.45, σ2 ≈ 9 / 1.349 ≈ 6.67.

Other rough heuristics (less reliable)
- Range rule of thumb for (roughly) bell-shaped data: range ≈ 6σ, so σ ≈ range/6.
- Whiskers are often not full min/max (they stop at 1.5·IQR), so range-based estimates are error-prone.

Better approaches (recommended)
- If you have the raw data: compute SD exactly.
- Python: numpy.std(x, ddof=1)
- R: sd(x)
- If you only have summary numbers (median, Q1, Q3, min, max, n), there are formulas to estimate mean and SD from those summaries (see Hozo et al. 2005 or Wan et al. 2014).
- To compare variability statistically, use tests:
- Levene’s test or Brown–Forsythe for equality of variances (robust to nonnormality).
- F-test (sensitive to normality).

Caveats
- The IQR→SD conversion assumes roughly normal shape. For skewed or heavy‑tailed distributions this will be wrong.
- Boxplots hide shape details; two plots with same IQR can have very different tails/outliers.

If you want, tell me:
- whether you have the raw data or only the boxplots,
- what sample sizes and what whisker rule was used,
and I can give a specific estimate or the code to compute exact SDs and run variance-comparison tests.