STATS Flashcards
The most widely used and known
probability distribution.
NORMAL DISTRIBUTION
Considered as the
cornerstone of modern statistics
NORMAL DISTRIBUTION
Often called a “Bell Curve” because it looks like a bell.
NORMAL DISTRIBUTION
Connotes the average in
ability, intelligence, size, emotional
traits, and personality.
NORMALITY
In plain language, most people and
things are ____ and are
embraced in the ____.
MEDIOCRE, MEAN CLASS
(1733) He developed
the mathematical
equation of the
normal curve but his
work went unnoticed.
ABRAHAM DE MOIVRE
(1809) He also
derived its equation of the
normal distribution from
a study of errors in
repeated measurements
KARL FRIEDRICH GAUSS
A continuous random variable
NORMAL DISTRIBUTION
Location Parameter
MEAN
Scale Parameter
STANDARD DEVIATION
Properties of the Normal Distribution
- CURVE IS BELL- SHAPED
- CURVE IS SYMMETRIC
- MEAN, MEDIAN, AND MODE CONCIDE IN THE CENTER.
- CURVE IS ASYMPTOTIC
- THE AREA OF THE CURVE IS 1.
The width of the curve is determined by the___.
STANDARD DEVIATION
Represents the distance
between a given measurement X and the
mean, expressed in standard deviation.
Z-SCORE
Table of Areas under the Normal
Curve
Z-SCORE
An unaltered measurement
RAW SCORE
Are the
activities which could be
repeated over and over again and
which have well-defined results.
EXPERIMENT
Is
the set of all outcomes in an
experiment
SAMPLE SPACE
Are the
possible results of an
experiment.
OUTCOMES
is a characteristic or attribute that can
assume different values.
VARIABLE
is a function that associates
a real number to each element in the sample space. It is a
variable whose values are determined by chance.
RANDOM VARIABLE
variable that has
a certain number of particular values and
nothing else.
DISCRETE VARIABLE
Properties of Discrete Probability Distribution
It represents the long-term
average or the central tendency of a
random variable’s possible outcomes when
an experiment is repeated many times.
EXPECTED VALUE OR MEAN OF A RANDOM VARIABLE
Any value that can be measured as
decimals or fractions. These are infinitely
situated between two values of reference.
CONTINUOUS VARIABLE
Often referred to as the expected value (E[X])
MEAN OF A RANDOM VARIABLE
Formula in getting the Mean or Expected
Value of the Discrete Random Variable.
E(X)= ∑ [x ⋅ P(x)]
STEPS IN FINDING THE MEAN OF THE DISCRETE
RANDOM VARIABLE.
- Determine the sample space.
- Count the number of random variables in each outcome in the
sample space and assign this number to this outcome. - Construct the probability distribution table.
- Multiply the value of the random variable X by the corresponding
probability. - Add the results obtained in Step 4. Results obtained is the mean of
the probability distribution.
Formula of Variance
VARIANCE(σ²) = ∑ [(x−μ)² P(x)]
