Math: Statistics and Combinatorics Flashcards
Mean
Average
(Sum of the Terms in a Set) / (NUmber of Terms in a Set)
Median
If set is Odd: The middle Term.
If set is Even: The average of the two middle terms.
Mode
The most frequently occurring values (the term or terms that appear the greatest number of times)
Range
The Difference between the largest value and the smallest value in a set
Standard Deviation
A Measure of the dispersion of data from the mean.
Order Matters
Permutations
_ N! _
(N-K)!
N = Number of Available Items to be arranged
K = The number of spots in which to arrange those items
Order Does Not Matter
Combinations
_ N! _
K!(N-K)!
N = Number of Available Items You Are Choosing From
K = The Number You Are Picking Down To
Letters in Alphabet
26
Common Factorial
0! = 1
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
Probability of a Single Event
P(A) = _ # of outcomes when A occurs _
# of total possible outcomes
Probability of Multiple Events
P(A and B) = P(A) * P(B)
Probability of Simultaneous Events
No Such thing exists in probability. Treat as Probability of Multiple Events (while keeping in mind dependent/independent elements).
Probability of One Event Or Another
Add the Probability of One Event Happening to the Probability of Another Event Happening. Subtract the Probability of Both Events Happening from this Sum.
P(A or B) = P(A) + P(B) - P(A and B)
If events are mutually exclusive, there is no need. to subtract since both events cannot occur together.
Number of Terms in an Inclusive Set
Range + 1
Largest Number - Smallest Number +1
Standard Deviation Functions
If multiply by # > 1, SD increases.
If divide by # >1, SD decreases.
Multiplying by -1, adding, and subtracting do not change SD.
