Statistics
Topics for Test 1
1. Descriptive Statistics
a. frequency charts
b. Histograms
c. Boxplots
e. Measures of Central tendency
I.
Mean
ii.
Median
iii.
Mode
f. Measures of Dispersion
i.
Variance
ii.
Standard Deviation
iii.
Range
Make sure you know the difference between population
and sample. Know the notation
2. Probability
a. Terminology : Sample space, event, mutually exclusive
independent
b. Basic probability formulas:
I.
P(AB) = P(A) + P(B) - P (AB)
ii.
If A and B are Mutually Exclusive, P(AB) = 0 and
P(AB) = P(A) + P(B)
iii.
P(A) = 1 - P(A’)
iv.
P(A|B)
v.
vi.
vii.
=
P(AB)
P(B)
P(AB) = P(A|B)P(B) = P(B|A)P(A)
A and B are independent if and only if
P(A|B) = P(A) or
P(AB ) = P(A)P(B)
0 < P(A) < 1
c. Some basic logical identities that might help you:
DeMorgan’s Laws
i.
P( (AB)’ ) = P( A’  B’ )
ii.
P( (AB)’ ) = P( A’B’ )
d. Remember :
P ( “at least one....” ) = 1 - P(“none”)
P(“neither A nor B “ ) means P(A’  B’)
e. Often probabilities are easiest to figure out if
if you make a chart or a tree diagram
f. Sensitivity / specificity of a test. Predictive value of a diagnostic test.
3. Random Variables
a. Discrete vs. Continuous random variables
b. Probability function (distribution) of a discrete random variable
Know the range, the probability function and be able to
represent the probability function as a picture
c. Expected value (mean) , Variance and standard deviation
of a discrete random variable
d. Discrete uniform distribution : mean and variance
e. Binomial distribution
I.
How to recognize
ii.
How to compute - formula and chart
iii.
Mean and variance
f. Poison distribution
I.
How to recognize
ii.
How to compute - formula and chart
iv.
Mean and variance
Make sure that you can solve problems with tree diagrams, charts, and
Venn(circle) diagrams.