Statistics for Traders #5: how to read skew off the tool's p25/median/p75 columns
On the NFP big_miss XAUUSD 15-minute bucket, the median lands at +78.6 pips, dead-centered within an IQR of [+44, +113]. Symmetric enough that you’d call it a normal-shaped middle. But the whiskers run to -46.6 on the min side and +345.67 on the max side — a right whisker 2.56× the length of the left. That’s skew, and the tool exposes it in two independent ways.
Stats #4 introduced the p25/median/p75 columns as a distribution-free way to describe FX bucket data. This post uses exactly the same columns to describe distributional asymmetry: which side of the median gets a longer tail, and which side gets a shorter one. Two independent signals to read, and they can — and do — disagree.
![Horizontal box-and-whisker chart. Two rows, each an NFP surprise bucket on XAUUSD 15m. Row 1 (top): big_miss n=9, IQR [+44.1, +113.3] as a coral filled bar, median +78.6 shown as a small vertical tick dead-centered inside the IQR bar, left whisker extending short from p25 to min at -46.6, right whisker extending far to max at +345.67. Row 2 (bottom): small_beat n=47, IQR [-136.17, +13.45] as a coral filled bar, median -49.3 shown as a small vertical tick that sits slightly toward the p75 side (right side) of the IQR bar, left whisker extending long from p25 to min at -352.2, right whisker extending shorter from p75 to max at +159.5. A dashed vertical zero line runs through both rows. Row 1 is annotated 'right-skew: whiskers only, IQR centered'; row 2 is annotated 'left-skew: BOTH IQR-position AND whiskers'.](/insights/stats-for-traders-skew/nfp-xauusd-buckets.png)
Signal 1: where the median sits inside the IQR
The IQR positionof the median tells you about the middle 50% of the data. In a perfectly symmetric distribution, the median sits exactly halfway between p25 and p75. If it’s closer to p25, the middle-of-the-distribution mass is packed on the low side and there’s more room to walk up to p75 — right-skew within the IQR.If it’s closer to p75, the mass is packed on the high side with a longer downward walk to p25 — left-skew within the IQR.
Formula, in plain terms:
median_position = (median - p25) / (p75 - p25) 0.5 = dead-centered (symmetric IQR) < 0.5 = median tilts toward p25 (right-skew within IQR: long right walk) > 0.5 = median tilts toward p75 (left-skew within IQR: long left walk)
On NFP big_miss XAUUSD 15m: (78.6 - 44.1) / (113.3 - 44.1) = 0.499. Dead-centered. The middle-50% shape says the bucket is symmetric.
On NFP small_beat XAUUSD 15m: (-49.3 - (-136.17)) / (13.45 - (-136.17)) = 0.581. The median tilts toward the p75 (right/high) side of the IQR. Which means the middle-of-the-distribution mass is packed on the high side, with more room extending downward to p25. That’s left-skew within the IQR.
Signal 2: whether the whiskers are the same length
The whisker asymmetry tells you about the outer 50% — the tails beyond the IQR. Symmetric-tailed distributions have (p25 - min) roughly equal to (max - p75). Fat right tail → right whisker much longer than left. Fat left tail → left whisker much longer than right.
left_whisker = p25 - min right_whisker = max - p75 ratio_R_over_L = right_whisker / left_whisker 1.0 = symmetric tails > 1.0 = right-skew via whiskers (long right tail) < 1.0 = left-skew via whiskers (long left tail)
On NFP big_miss XAUUSD 15m: left whisker 44.1 - (-46.6) = 90.7p. Right whisker 345.67 - 113.3 = 232.4p. Ratio 2.56×. Strongly right-skewed via whiskers, even though the IQR was centered. The +345p print from March 2026 (a -92k NFP that came in against a +58k consensus) dominates that right whisker single-handedly.
On NFP small_beat XAUUSD 15m: left whisker -136.17 - (-352.2) = 216.03p. Right whisker 159.53 - 13.45 = 146.08p. Left/right ratio 1.48× — left-skewed via whiskers. The min at -352.2p (from a July 2025 small NFP beat) extends the left tail well beyond what the p25 alone suggests.
The two signals together
| NFP bucket (XAUUSD 15m) | n | Median in IQR | R/L whisker | Skew interpretation |
|---|---|---|---|---|
| big_miss | 9 | 0.50 | 2.56× | IQR symmetric; strong RIGHT-skew via whiskers |
| small_beat | 47 | 0.58 | 0.68× | BOTH signals point LEFT-skew (long left tail) |
Two buckets, two very different skew stories. On big_miss, the middle 50% of outcomes is symmetric — the median +78.6p is a fair description of “where you’ll usually land”. But the tails are strongly right-skewed: the biggest observed print produced +345.67p, three median's worth of upside above p75. On small_beat, both the IQR position and the whiskers agree — the pair is mass-on-the-right with a long left tail extending to -352.2p. When both signals point the same way, you can trust the story more strongly.
The nine big_miss prints, individually
Since the sample is small, they’re listable. Sorted by 15m move:
2017-10-06 -33k vs +82k fc z=-2.93 -46.60p ← min 2020-04-03 -701k vs -100k fc z=-10.21 +1.90p (COVID whipsaw) 2019-03-08 +20k vs +180k fc z=-2.14 +44.10p ← p25 2011-06-03 +54k vs +161k fc z=-1.55 +61.80p 2021-09-03 +235k vs +720k fc z=-1.85 +78.59p ← median 2013-04-05 +88k vs +198k fc z=-1.99 +108.70p 2014-01-10 +74k vs +196k fc z=-2.42 +113.30p ← p75 2016-06-03 +38k vs +159k fc z=-2.34 +201.60p 2026-03-06 -92k vs +58k fc z=-3.36 +345.67p ← max
The +345.67pMarch 2026 max was a genuinely-negative NFP (-92k printed, +58k expected) landing during an already-shaky risk-off tape — gold ripped. It’s a real observation, not a data error, and it’s the single print doing all the whisker-skew work on this bucket. Removing it would drop the R/L ratio to roughly 0.98× (nearly symmetric), which is a useful sensitivity check: the skew story rests on one recent observation.
How to use skew at the sizing table
Three practical reads that flow from the two signals.
Right-whisker skew warns you to widen your take-profit on the correct-direction side.On NFP big_miss XAUUSD, the median target is +79p but the recent max is +345p. That doesn’t say every big_miss will produce +345p; it says that when the print looks like the outlier setup (a negative NFP against a positive consensus, on a risk-off tape), leaving room to trail the take-profit past the median is worth considering.
Left-whisker skew warns you to widen your stop on the correct-direction side too.On NFP small_beat XAUUSD, the median target for a short is -49p, but the max downside (from the trader’s perspective, best case) has been -352p. Anchoring a target at -49p means you’re systematically exiting before the fat left tail plays out on the ~1-in-14 prints that reach it.
When the two signals disagree, weight IQR-skew. The whiskers are informed by min and max — single extreme observations that can be dominated by one anomalous print. The IQR position is informed by p25 and p75 — order-statistics that smooth over the outliers. If a bucket has IQR-symmetric and whisker-skewed, it’s usually one recent outlier driving the whisker story, and the base-case shape is still symmetric. Trust the middle more than the edges.
What this doesn’t say
Skew is not the same as fat tails. A distribution can be symmetric but heavy-tailed (both whiskers long relative to the IQR — kurtosis, a topic for another day). A distribution can also be skewed but light-tailed (short but asymmetric whiskers). Skew is only about asymmetry; the length of the tails is a separate diagnostic.
Small-n caveat still applies. The big_miss bucket at n=9 has whisker positions that depend heavily on one or two extreme prints. Adding or removing one observation can shift the ratio dramatically (the sensitivity check on the +345p March 2026 print above is exactly that exercise). Treat tail-bucket skew ratios as directional signals, not point estimates.
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