STATISTICS AND PROBABILITY TERMINOLOGIES Flashcards
● variable that assigns a numerical value to each
outcome of a random event.
RANDOM VARIABLE
TWO TYPES OF RANDOM VARIABLE (DC)
DISCRETE
CONTINUOUS
○ a variable whose value is obtained through counting.
Discrete Variable
○ variable whose value is obtained through measurement.
Continuous Variable
⤻ is the set of all possible outcomes in an experiment.
Sample Space
{HHH, TTT, HHT, HTT, THH, TTH, HTH, THT}
Sample Space
X = {0, 1, 2, 3}
Range Space
probability of x
P(x)
values of possible outcomes
x
⤻ values obtained from functions that assign real number
to each point of a sample space.
possible values of a random variable
also known as discrete probability distribution
PROBABILITY MASS FUNCTION (PMF)
The Properties of a Probability Distribution (2)
○ Nonnegativity
○ Norming Property
the probability of each value of the random variable
must be between or equal to 0 and 1
Nonnegativity
sum of the probabilities of all values of the random
variable must be equal to 1.
Norming Property
0≤P(X)≤1
Nonnegativity
ƩP(X)=1
Norming Property
a probability distribution with only two possible
outcomes: success and failure
binomial distribution
average value of all the outcomes.
mean
E(x)
expected value
x
random variable
f(x)
probability of x
μ
average
P(x)
probability of x
describes the average square deviation of
the variable from the mean.
variance
σ^2
symbol for variance
σ
symbol for standard deviation
the square root of the variance
standard deviation
● also known as normal curve.
● provides a graphical representation of statistical values
that are needed in describing the characteristics of
populations as well in making decisions.
● mean, median, and mode are equal.
NORMAL DISTRIBUTION
graph of normal distribution
NORMAL CURVE
CHARACTERISTICS OF A NORMAL DISTRIBUTION
- The distribution curve is (the normal probability
distribution) bell –shaped. - The curve is symmetrical about its center.
- The mean, median and the mode coincide at the
center. - The width of the curve is determined by the standard
deviation of the distribution. - The tails of the curve flatten out indefinitely along the
horizontal axis, always approaching the axis but
never touching it. That is, the curve is asymptotic to
the base line. - The area is under the curve is 1. Thus, it represents the
probability or proportion or the percentage associated
with specific sets of measurement values.
the standard normal curve is a:
○ mean μ = 0
○ standard deviation σ = 1
height of the particular values of X
Y
any score in the distribution
X
standard deviation of the population
σ
mean of the population
μ
3.1416
2.7183
e
FINDING THE AREAS OF A NORMAL CURVE GIVEN A Z – VALUE
- Express the given z-value into a three digit form.
- Using the z-table, find the first two digits on the left column.
- Match the third digit with the appropriate column on the right.
- Read the area (or probability) at the intersection of the
row and the column. This is the required area.
● a statistical rule which states that for a normal
distribution, almost all observed data will fall within
three standard deviations of the mean or average
EMPIRICAL RULE
— provides the proportion of the area (or
probability or percentage) between any two specific
values under the curve.
Z - TABLE
● number of standard deviation away from the mean.
Z - SCORE
a point in the distribution such that a given number of
cases is below it.
PERCENTILE
each of ten equal groups into which a
population can be divided according to the distribution
of values of a particular variable.
DECILES
are three values that split sorted data
into four parts, each with an equal number of
observations.
QUARTILES
a part of the sampling technique in which each sample
has an equal probability of being chosen.
RANDOM SAMPLING
a selection of a subset of a population where each
element has an equal chance of being selected.
Simple Random Sampling
a selection of a subset of a population where each
element has an equal chance of being selected.
Systematic Random Sampling
selection of a simple random sample from each of a
given number of a subpopulations, or strata.
Stratified Random Sampling
○ a selection of clusters from the available clusters in the
population.
Cluster Sampling
samples are selected based on the needs of the study
Purposive Sampling
a researcher chooses a possible respondent. Then,
each respondent is asked to give recommendations to
other possible respondents
Snowball Sampling
population is divided into predefined control categories.
Quota Sampling
the totality of observations, items, things, or people under consideration.
⤻ represented by letter “N”
population
a subset of the population.
⤻ elements taken from a population
⤻ represented by small letter “n”
sample
→ any measurable characteristic of a population.
PARAMETER
→ any measurable characteristic of a sample.
STATISTIC
is a frequency distribution using the means computed from
all possible random samples of a specific size taken
from a population.
sampling distribution of sample means
— difference between the sample mean and the population mean.
sampling error
μ = Ʃx
N
Population Mean
σ^2= Ʃ (x-μ)^2
N
Population Variance
σ= √Ʃ (x-μ)^2
N
Population Standard Deviation
: nCr = n!
r! (n-r)!
All Possible Samples
μx̄=Ʃx̄
N
Mean of Sampling Distribution of Mean
σ^2x̄= Ʃ (x̄- μx̄)^2
n
Variance and Standard Deviation of the Sampling
Distribution of Mean.
the arrangement of items which order matters
Permutation
Selection of items which order does not matter
Combination
