Quartiles and Percentiles - Measures of Central Tendency, Business Mathematics & Statistics Video Lecture - Business Mathematics and Statistics - B Com

for this lecture I'm going to be talking
about organizing data into percentiles
and quartiles but first of all I want to
talk about percentages imagine we have a
data set like this very simple one two
three four and five I could ask you a
question like how many numbers are even
well it's pretty obvious the two and the
four are even but we could make that
into a percentage a percentage is
basically the number of things meeting
the characteristic of interest divided
by the total number of observations
times 100 so that might sound kind of
weird but let me show you this the
characteristic of interest is even there
are two even numbers divided by five
total observations so 2 divided by 5
times 100 is 40 we could say that 40
percent of the numbers in this data set
are even and that would be a percentage
now a percentile is a value below which
a certain percentage of the observations
lie so let me show you what that means
here's a longer data set goes from 2 to
3 all the way up to 11 12 now I could
ask you what is a percentile ranking of
10 so we have 10 basically I want to
know what percentage of scores lie below
that so all these things that I have
here in blue are scores that are below
10 so for the question of what is
percentile ranking of 10 we can use this
equation the percentile ranking of any
value is equal to the number of values
below that value divided by the total
number values in the set times 100 so
there are 16 blue numbers below 10 and
there are 20 total numbers so 16 divided
by 10 times 100 is 80% the percentile
rank of the value 10 is 80% because 80%
of the scores lie below it so now we can
kind of work backwards what value exists
at the percentile ranking of 25% so
we're asking basically what score has
25% of the scores below it so we can use
this equation to find out what value
number is
basically the percentile divided by 100
s multiplied by the sample size plus 1
so when should in the 25th percentile so
I do 25 divided by 100 times 20 plus 1
because we have 20 scores and when I
work all that out I get a value of 5
point 2 5 but let's definitely make any
sense I mean there could be a 5th value
or a 6 value but there is no 5.25 the
value so if you end up with something
like that that isn't a whole number you
can just take the average of in this
case the 5th and the 6 and whatever that
averages that is what exists at the 25th
percentile so my 5th number is 5 and my
6 number is 5 so the average of those
two numbers the mean of those two
numbers is obviously 5 so for the
question what value exists at the
percentile ranking of 25% the answer is
5 now one more quick thing quartile is
is pretty simple imagine you have your
data organized into a line like this
25% represents the first quartile 50%
represents the second quartile and 75%
represents the third quartile so if
anyone is talking about quartiles that's
really what they're talking about that
is talking about these three different
percentile rankings and that's it for
this lecture understand what percentiles
are what quartiles are and what
percentages are