Summary Formula Sheet Statistics (BT1111) 26th Dec 2022

Statistics Cheat Sheets

Descriptive Statistics:
Term Meaning Population Formula Sample Formula Example
{1,16,1,3,9}
Sort Sort values in {1,1,3,9,16}
increasing order
Mean Average N n 6
 Xi X 1  X 2  ...  X n
 Xi
i 1 i 1
 X 
N n n
Median The middle value 3
– half are below
and half are above
Mode The value with the 1
most
appearances
Variance The average of (1-6)2 + (1-6) 2 +
 X i  X 
n
1 N 2
the squared 2   X i   2 (3-6)2 + (9-6)2 +
N i 1 i 1
deviations s2  (16-6)2 divided by
n1
between the 5 values = 168/5
values and the = 33.6
mean
Standard The square root of   2 Square root of
 X i  X 
n
2
Deviation Variance, thought 33.6 = 5.7966
i 1
of as the s  s2 
“average” n1
deviation from the
mean.
Coefficient The variation s 5.7966 divided by
CV 
of relative to the X 6 = 0.9661
Variation value of the mean
Minimum The minimum 1
value
Maximum The maximum 16
value
Range Maximum minus 16 – 1 = 15
Minimum

Probability Terms:
Term Meaning Notation Example* (see footnote)
Probability For any event A, probability is represented within 0  P() 0.5
P 1.
Random A process leading to at least 2 possible outcomes Rolling a dice
Experiment with uncertainty as to which will occur.
Event A subset of all possible outcomes of an experiment. Events A and B
Intersection of Let A and B be two events. Then the intersection of AB The event that a 2
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, Statistics Cheat Sheets

Events the two events is the event that both A and B occur appears
(logical AND).
Union of Events The union of the two events is the event that A or B AB The event that a 1, 2, 4, 5
(or both) occurs (logical OR). or 6 appears
Complement Let A be an event. The complement of A is the event A The event that an odd
that A does not occur (logical NOT). number appears
Mutually A and B are said to be mutually exclusive if at most A and B are not mutually
Exclusive one of the events A and B can occur. AB=0 exclusive because if a 2
Events appears, both A and B
occur
Collectively A and B are said to be collectively exhaustive if at A and B are not
Exhaustive least one of the events A or B must occur. collectively exhaustive
Events because if a 3 appears,
neither A nor B occur
Basic Outcomes The simple indecomposable possible results of an Basic outcomes 1, 2, 3, 4,
experiment. One and exactly one of these outcomes 5, and 6
must occur. The set of basic outcomes is mutually
exclusive and collectively exhaustive.
Sample Space The totality of basic outcomes of an experiment. {1,2,3,4,5,6}
* Roll a fair die once. Let A be the event an even number appears, let B be the event a 1, 2 or 5 appears




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