Data Analysis Flashcards
Relative frequency
Frequency / Total
Areas of a bar graph or areas under a distribution spread
1
Standard deviation formula
(Average(Mean-Value)^2)^1/2
- Calculate means of values
- Find difference between mean and each value
- Square each difference
- Find average of squared differences
- Non-negative square root of the average of the squared differences
Most values are within how many standard deviations of the mean?
3
Intersection of sets S and T
S (upside down U) T
Union of sets S and T
S U T
If sets S and T are disjoint/mutually exclusive, then what does their intersection equal?
0
If sets S and T are disjoint/mutually exclusive, then what can their probabilities not equal?
0
Inclusion-exclusion principle
|A union B| = |A|+|B|-|A intersection B|
|B union C| = |B|+|C| because |B intersection C| = 0
Multiplication principle
First choice possibilities x second choice possibilities
Permutation
Order matters
nPk = n! / (n-k)!
n >/= k
N-Factorial
Common type of permutation
n! = n(n-1)! = n(n-1)(n-2)! = n(n-1)(n-2)(n-3)!…
Combination
Order does not matter
Combination = Permutation / Number of ways to order
nCk = n! / k! (n-k)!
nCk = nCn-k
nC0 = 1
nCn = 1
Probability of an event
of outcomes in the event / # total possible outcomes
If P(E) = 1, then
E is certain to occur
If 0 < P(E) < 1, then
E is possible but not certain to occur
P(E not happening)=
1 - P(E)
If E is an event, then the probability of E equals
The sum of the probabilities of the outcomes in E
The sum of the probabilities of all possible outcomes of an experiment
1
The event that both E and F occur
E intersection F
The event that E or F, or both occur
E union F
P(E or F)
P(E) + P(F) - P(E and F)
P(E and F) = P(E)P(F)
P(E or F) if E and F are mutually exclusive
P(E) + P(F)
P(E and F) if E and F are independent
P(E)P(F)
If P(E) and P(F) do not equal 0, then
E and F cannot be both mutually exclusive and independent
P(E and F) if E and F are mutually exclusive
0
2/3 of data is within how many standard deviations of the mean?
1
Almost all data is within how many standard deviations of the mean?
2
Probability distribution is equal to
the Relative frequency distribution
The slope of a line
Average of means
Normal distribution mean, median, mode
Nearly equal
