Relative Frequency Theory of probability, Business Mathematics and Statistics Video Lecture | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

hi this tutorial covers relative
frequency probability sometimes also
known as the empirical method for
calculating probability so there are
three ways to make a probability
statement the first being theoretical
probability also known as the a priori
method experimental probability also
known as relative frequency probability
and sometimes referred to as the
empirical method and the third one is
subjective probability so we're going to
spend most of the time here talking
about experimental probability and at
the end of the tutorial we'll touch on
subjective probability but we're not
going to spend a lot of time discussing
that okay so let's start with a
definition so experimental probability
or relative frequency probability these
two terms can be used interchangeably is
a method of calculating probability
where the probability is the ratio of
the number of trials where the desired
event occurs to the number of total
trials okay and this is usually going to
be in the long run so they're going to
give you data that has occurred in the
long run and you're going to calculate a
probability based on that and again this
is also known as the empirical method of
calculating probability so the
probability of an event e P of e okay
remember that this is probability
notation so this stands for the
probability of event can be found by the
probability of E is approximately equal
to the number of times a occurs divided
by the number of trials okay so we're
going to be using existing data to be
making probability statements okay so
let's take a look at an example
so consider a frequency distribution for
a sample of patients in an orthopedic
clinic okay so what um what they did is
they collected the heights and put them
into intervals so we have 4 6 2 5 feet 5
feet 2 5 6 5 6 2 6 feet 6 feet 2 6 6
okay we have the frequencies of patients
that have come in so this is notice
there's a lot of a lot of patients here
so this is data that's been accumulating
for some time so the chance experiment
is a reception
notes the height of the next patient
that enters the clinic okay we're going
to let event e be the event of observing
a patient in the five foot six to six
feet height interval then we want to
know what's the probability of e so
basically what we're doing with relative
frequency probability is we're using
frequency data that's already been
collected and using that to make a
prediction about the probability of some
event okay so if we're calculating
probability of e the probability of E is
going to approximately be equal to so
let's actually use a squiggly equal
equal sign here the total number of
trials needs to go on the bottom okay so
what we need to do to calculate the
number of trials is go to the calculator
and add up all of those frequencies so
five twelve plus twenty one eighty nine
plus seventeen ten plus four twenty
three okay and if we add those all up
it is about forty eight thirty four okay
so that goes on the bottom of the
fraction so that's how many observations
there were and then the number of times
he occurs or it has occurred so that
value is this 1710 okay so that is my my
probability there so now what I want to
do is I want to divide those two numbers
so 17 10 divided by 48 34 okay and to
get that as a decimal value I'm going to
round it to the nearest thousandth so it
would be approximately equal to 0.5 or
soomi point three five four okay so we
think about that in terms of percent
that means that there's about a thirty
five percent chance that the next person
that walks through the door will have a
height between five foot six and six
feet okay
so again that was calculating
probability of an event using relative
frequency
okay and as promised let's just talk a
little bit about subjective probability
subjective probability is a probability
statement that an individual makes based
on a personal judgement to describe the
likelihood of an event so this isn't
really using any sort of statistical
reasoning it's just based on somebody's
judgement so this subjective probability
doesn't really belong in a statistics
class but you do see these statements
quite a bit so example I have an 85
percent chance of passing my statistics
exam so maybe I'm using a little bit of
reasoning to come up with that 85
percent but it's not really it's really
just based on my own judgement so
subjective probability again is you hear
that all you hear subjective
probabilities a lot but just know that
those aren't really based on sound
statistical reasoning so that has been
the tutorial on relative frequency
probability thanks for watching