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
This is what was actually asked about.
- 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
- +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%
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”.