# how to explain a percentile

On my app, users get a score. I want to tell them where they stand relative to other users. I have a feature that tells them they are in first place, second place... nth place.

I would also like to tell users which percentile they are in. E. g. "you are in the 10th percentile". My problem: this on its own is ambiguous. Are they in the 10th percentile from the top, or the bottom? Is it better to express this in terms of how far they are from the top or from the bottom?

What is the right wordage here? Some ideas I have:

1. "You are in the top 10% of users"
2. "You are better than 90% of users"
3. "You are in the 90th percentile"

• You need no to use statistical terms, like percentiles, etc. for average users. The test is simple: if something needs to be explained, just replace it. "Top 10% of users" sounds much better. Jun 21, 2016 at 21:40
• Thanks all for answers - I have an additional question for which I would appreciate input: How do I report the percentile where the goal is to decrease score? For instance, 10 golfers have scores 80,79,78,77,76,75,74,73,72,71 - would it be accurate to say that the golfer with the score of 71 is in the 91st percentile or in the 9th percentile? Jul 11, 2016 at 21:17

In SAT terms, a person's percentile rank is the percentage of students who score lower on the SAT. To the extent your audience is familiar with the usage of the word percentile from experience with the SAT, that is a reasonable working definition.

I agree with Alexey Kolchenko that academic terminology like percentile is potentially confusing. You might try stating their rank in terms like "better than 7 out of 10 people." If the difference between 70% and 72% matters and you are able to measure well enough to distinguish that level of precision, then state their rank as "better than 71 out of 100 people."

• OP's 3rd option is correct under the SAT convention, except that it should read "you are in the 91st percentile" since the user ranks above 90% of users. Jun 22, 2016 at 4:04

I assume that all languages can qualify a better and a worse half, most should also be able to state that something or someone is neither really good nor really bad, but mediocre. Many languages, like English, also have separate lexemes for good and bad or top and bottom (cf. Latin altus which means either ‘high’, e.g. a mountain, or ‘low’, e.g. a valley) and a lot of them know morphological or syntactical comparation, e.g. good, better, best and bad, worse, worst, which often can be used either in an absolute (scalar) or a relative (ordinal) sense. Few will also support that for the middle ground, i.e. mediocre, more mediocre, most mediocre do not signify slightly better or worse than median qualities, but at best narrower bands around the middle. Some languages will allow words for ‘zero’ / ‘none’ and ‘all’ / ‘full’ / ‘complete’, though. In conclusion, few languages (if any) will provide the means to distinguish 10 quality levels unambiguously and harmonically, but you can hope for 9. This fits well with directions or unmarked radial gauges, where we intuitively distinguish 4 levels (like North, East, South, West or 3, 6, 9, 12 o’clock) and can improve this by halving each segment, everything finer requires labels or marks (as on a clock face with its 12 to 60 intervals).

I think that top / upper, bottom / lower and medium / mediocre / central work better for median-based percentiles and absolute counts than best / better, worse / worst and middle, which I’d use for groups based on the average/mean.

Still, we can try to work our way up as the distinctions grow finer.

## Descriptions for quartiles

• Q4: Top Quarter, (Best Quarter), Top 25%
• Q3: Top Half, Upper Half, (Better Half), Top 50%
• Q2: Bottom Half, Lower Half (Worse Half), Bottom 50%, Top 75%
• Q1: Bottom Quarter, Lowest Quarter, (Worst Quarter), Bottom 25%

• Also IQR = Q2 + Q3: Medium 50%, (Middle 50%) – a blown up middle third

## Descriptions for quintiles

• (Best), Top, Top 20%
• (Better), Upper, Top 40%
• (Middle), Mediocre, Top 60%
• (Worse), Lower, Bottom 40%, Top 80%
• (Worst), Bottom, Bottom 20%

## Descriptions for deciles

• Top 10%, Better than almost all users
• Top 20%, Better than 4 in 5, Top Quarter (approximated), Better than 3 in 4
• Top 30%, Top Third (approximated), Better than 2 in 3
• Top 40%, Better than 3 in 5
• Above most users, Better than most users, Top Half, Upper Half, (Better Half), Top 50%
• Bottom 50%, Top 60%, Bottom Half, Above a lot of users, Below most users
• Bottom 40%, Top 70%, Above many users
• Bottom 30%, Top 80%, Bottom Third (approximated), Above some users
• Bottom 20%, Bottom Quarter (approximated), Above few users
• Bottom 10%, Below almost all users

## Standard deviations

• +2 σ: Top 0.0032% (= Top Ten of ca. 300’000 users)
• +1.5 σ: Top 0.135% (= Top Ten of ca. 7’500 users)
• +1 σ: Top 2.28% (= Top Ten of ca. 450 users)
• +0.5 σ: Top 15.9% (= Top Ten of ca. 60 users)
• ±0 σ: Mean (not median)
• −0.5 σ: Bottom 15.9%
• −1 σ: Bottom 2.28%
• −1.5 σ: Bottom 0.135%
• −2 σ: Bottom 0.0032%

## Recommendation

I would suggest to use an approach similar to Stack Exchange: Show the most positive sounding, encouraging figure, mixing relative and absolute measures, e.g. “Top Ten Today”, “Week Top 100”, “Most active 10% this month”, “Best 5% this quarter”, “Upper half this year”, “Hall of Fame: Top 100 of all time”, “More points than a lot of people”.