Econ 325

Front 1

Data

Back 1

a set of numeric observations

Front 2

Population

Back 2

The complete set of numeric observation

Front 3

Sample

Back 3

an observed subset of observations taken from the population

Front 4

Variable

Back 4

any characteristic of a population or sample that is ofinterest to study.

Front 5

Quantitative variables

Back 5

Continuous, Discrete

Front 6

Continuous

Back 6

the numeric observations can take anyvalue in some interval

Front 7

Discrete

Back 7

the numeric observations can take a limitednumber of values

Front 8

Units of measurement for quantitative variables

Back 8

Levels:

Proportions:

Percentages:

Front 9

Qualitative/Categorical variables

Back 9

responses do not have anumerical meaning

Front 10

n

∑b=

i=1

Back 10

n*b

Front 11

n

∑b*xi=

i=1

Back 11

n

b∑xi

i=1

Front 12

∑ƒ(x)

x

Back 12

the summation over all values of x in f(x)

Front 13

Population mean

Back 13

N

a parameter denoted as µ = (1/N)*∑xi

i=1

Front 14

Sample mean

Back 14

_ n

a statistic denoted as x=(1/n)*∑xi

i=1

the average is generally referring to the sample mean

Front 15

Sample median

Back 15

the middle value of the sample observations. sort the observations and then find the middle value.

Front 16

Mode

Back 16

the numerical value that occurs most frequently.

Front 17

Geometric mean

Back 17

_ n

x=(∏xi)^(1/n)

g i=1

for data sets with positive observations

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range

Back 18

maximum-minimum

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variance

Back 19

_ _ _

(x₁-x)², (x₂-x)², (x -x)²

n

Front 20

sample variance

Back 20

n _

s²=(1/n-1)∑(xi-x)²

i=1

if sample size n is relatively large then

n _ n _

s²=(1/n-1)∑(xi-x)² ≅s²=(1/n)∑(xi-x)²

i=1 i=1

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sample standard deviation

Back 21

s=√s²

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Population variance

Back 22

N

δ²=(1/N)∑(xi-µ)²

i=1

Front 23

Population standard deviation

Back 23

δ=√δ²

Front 24

Sample coefficient of variation

Back 24

_ _

s/x or s/x*100

meaningful if all observations in the data set are positive

Front 25

Interquartile range

Back 25

Q₃-Q₁

gives the spread of the middle 50% of observations

Front 26

Sample Covariance

Back 26

a measure of the linear association between two variable

n _ _

s= (1/n-1)∑ (xi-x)(yi-y)

xy i=1

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Sample Correlation

Back 27

r=Sxy/(SxSy)

A result should be between -1 and 1

as|r| gets closer to one the stronger theevidence for a linear relationship between the two variables.

r > 0 indicates a positive linear relationship

r < 0 indicates a negative linear relationship

r= 0 indicates no linear relationship –the variables are uncorrelated

r= 1 gives a perfect positive linear relationship –the observations exactly fit on an upward slopingstraight line.

Front 28

Sample Space

Back 28

The set of all basic outcome

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Event

Back 29

A subset of basic outcomes from the sample space

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A∩ B

Back 30

Intersection of A and B, the set of all basic outcomes in the sample set that are in both A and B

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Mutually Exclusive

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sets that share no common basic outcomes i.e. where A∩ B is an empty set

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A∪ B

Back 32

This is the set of basic outcomes that are in either A or B or both

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collectively exhaustive

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When the union of several events gives the whole sample space

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complement of A

Back 34

denoted by A . is the set of basic outcomes in the sample space S that do notbelong to the event A

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relative frequency

Back 35

theproportion of occurrences of outcome the event in n trials is n₁/n and as n gets larger we can say that the relative frequency is approximately equal to the probability

Front 36

how many combinations of x objects with no repetitions

Back 36

x!

Front 37

The number of permutations

Back 37

The number of possible orderings of x chosen from n where n>x

denoted n

P = n!/(n-x)!

x

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repetitions allowed ordering

Back 38

The number of possible orderings of x chosen from n where n>x with repetitions is

x

n

Front 39

the number of combinations

Back 39

from n objects choose x objects (n > x),repetitions not being allowed and different orderings of the same xobjects not being counted separately. denoted

n n

C = 1/x! * P = n!/(x!(n-x)!)

x x

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conditional probability

Back 40

The probability of A given B

P(A|B)

when the number of attempts n is large enough

nA ∩ B/n is approximately= P(A|B)

(the amount of time A and B both occured divided by the amount of attempts)

also

P(A|B) = P(A∩B)/P(B)

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Statistically Independent

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P(A∩B)=P(A)*P(B)

P(A|B)=P(A)

P(B|A)=P(B)

Information about event B is no use in determining theprobability of event A and vice versa

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Bayes’ Theorem

Back 42

P(B|A)=(P(A|B)P(B))/P(A)

Front 43

Random Variable

Back 43

a variable that takes on numerical outcomesdefined over a sample space of a random experiment

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probability distributionfunction

Back 44

P(x) = P(X= x)

Front 45

cumulative probability function

Back 45

F(a) = P(X≤a)

do a summation of pdf over all possible values of x less than or equal to a