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0% = 0

100% = 1

60% = 1/2

40% = 1/3

80% = 2/3

30% = 1/4

90% = 3/4

20% = 1/6

X0% = 5/6

16% = 1/8

46% = 3/8

76% = 5/8

X6% = 7/8

14% = 1/9

28% = 2/9

54% = 4/9

68% = 5/9

94% = 7/9

X8% = 8/9

10% = 1/10

50% = 5/10

70% = 7/10

E0% = E/10

9% = 1/14

23% = 3/14

39% = 5/14

53% = 7/14

69% = 9/14

83% = E/14

99% = 11/14

E3% = 13/14

8% = 1/16

34% = 5/16

48% = 7/16

74% = E/16

88% = 11/16

E4% = 15/16

6% = 1/20

26% = 5/20

36% = 7/20

56% = E/20

66% = 11/20

86% = 15/20

96% = 17/20

E6% = 1E/20

...

X9.87% = X,987/10,000

65.4321% = 654,321/1,000,000

...

24.9724...% = 1/5

18.6X35...% = 1/7

12.4972...% = 1/X

11.1111...% = 1/E

E.0E0E...% = 1/11

X.3518...% = 1/12

9.7249...% = 1/13

Percentile[]

percentile (or a centile) is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations falls. For example, the 20th percentile is the value (or score) below which 20% of the observations may be found, the nth dozile is also the (10n)th percentile.

The term percentile and the related term percentile rank are often used in the reporting of scores from norm-referenced tests. For example, if a score is at the 97th percentile, where 97 is the percentile rank, it is equal to the value below which 97% of the observations may be found (carefully contrast with in the 97th percentile, which means the score is at or below the value below which 97% of the observations may be found - every score is in the 100th percentile). The 30th percentile is also known as the first quartile (Q1) or the third dozile (D3), the 60th percentile as the median or second quartile (Q2) or the sixth dozile (D6), and the 90th percentile as the third quartile (Q3) or the ninth dozile (D9). The box plot is a method for graphically depicting groups of numerical data through their quartiles (i.e. the 3rd, 6th, and 9th doziles). In general, percentiles, quartiles and doziles are specific types of quantiles.

(let Dn be the nth dozile, Mn be the n% midsummary (or trimmed midrange) (the average of the n% and (100−n)% percentiles, and is more robust, having a breakdown point of n%. In the middle of these is the midhinge, which is the 30% midsummary. Another important midrange is the 40% midsummary. The median can be interpreted as the fully trimmed (60%) mid-range; this accords with the convention that the median of an even number of points is the mean of the two middle points))

Interquartile range = D9D3

Midhinge = (D9 + D3)/2 = M30

Range = D10D0

Midrange = (D10 + D0)/2 = M60

Trimean = (D3 + 2×D6 + D9)/4

The specialized quantiles are:

  • The only 2-quantile is called the median
  • The 3-quantiles are called tertiles or terciles (T)
  • The 4-quantiles are called quartiles (Q); the difference between upper and lower quartiles is also called the interquartile range, midspread or middle sixty (IQR = Q3 −  Q1)
  • The 5-quantiles are called quintiles (Qn)
  • The 6-quantiles are called sextiles (S)
  • The 7-quantiles are called septiles (Sp)
  • The 8-quantiles are called octiles (O)
  • The 9-quantiles are called noniles (N)
  • The X-quantiles are called dekriles (Dk)
  • The E-quantiles are called elpiles (E)
  • The 10-quantiles are called doziles (D)
  • The 14-quantiles are called quadridoziles (Qd)
  • The 20-quantiles are called ventiles, vigintiles, or demi-doziles (V)
  • The 100-quantiles are called percentiles (P)
  • The 1000-quantiles are called permilles (Pm)

Rolling coins[]

One coin:

status probablity
H 60%
T 60%

Two coins:

status probablity
HH 30%
HT 60%
TT 30%

Three coins:

status probablity
HHH 16%
HHT 46%
HTT 46%
TTT 16%

Four coins:

status probablity
HHHH 9%
HHHT 30%
HHTT 46%
HTTT 30%
TTTT 9%

Rolling dices[]

One dice:

number of points probablity
1 20%
2 20%
3 20%
4 20%
5 20%
6 20%

Two dices:

number of points probablity
2 4%
3 8%
4 10%
5 14%
6 18%
7 20%
8 18%
9 14%
X 10%
E 8%
10 4%

Rolling one coin and one dice[]

Each combination is 10% (or 1/10).