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okay so whenever we've got cumulative
frequency it's um the numbers are
accumulating as they're going along so
we adding them up as we're going along
is a running total
so
this is up to 10 so everything up to 10
so what's up to 10 just this first one
so just five is up to 10 the second box
is up to 20 so everything up to 20 so
it's both of these two boxes together so
we're adding on the 10 so that makes 15.
then up to 30 is all three of these
so we're adding on another 10
so 25
then up to 40
add on the 16
so that makes it 41
up to 50 as my next one
46 and add on the last one
to 50. so that's cumulative frequency
that's adding up as we go along that's a
running total
so when we're asked to plot the
cumulative frequency graph
this is up to 10 this 5 is up to 10 so
we're plotting this top number we don't
plot the midpoint because there haven't
been five by time we get halfway five
there's only been five by time we get to
ten
so we plan top point cumulative
frequency so these are the points you
wanna plot
so we're playing 10 against 5 on
cumulative frequency
so that's in the middle there
20 15 so
15 should be in there
30 against 25
40 against 41
50 against 46
and 60 against 50.
and then when we join them up it should
be a smooth curve
so a curve that joins up all these
points
so
hopefully i won't mess this up
i've missed a point there but um
we want to join up the smoothest curve
we possibly can
and then they could ask us questions
like finding the median from here
so if there's
50 people 50
numbers in our
on our graph and the median
is halfway so they're made to be 25
so what we'd be looking for is 25th
person
and
we'll go along to there and go down so
the median in this case
is 30.
let's have a look at a different one
so
here's presented differently but we're
still going to do the same thing
cumulative frequency is still a running
total
so we'll put cumulative frequency in
this box and we're going to add them up
as we go along so 6
and then we're going to add on the next
one so 6 plus 9
makes 15
plus 24
makes 39
plus 16
55
plus 9
61
864
plus 670
so
these numbers are up to 70.
um
and when we plot them we're going to
plot
top point against cumulative frequency
always the top point
so
10
against six
so ten goes with six
twenty fifteen
30 39
40 55
and 50 goes to 64.
up there
and 60 years of 70
and then we join up again with a smooth
curve
so
up like that
and
smooth curve joining all the points
so then we're asked to find the median
so
if there's 70 people say 70 on the
frequency 70 um
we want halfway which is 35.
so
again with a ruler if we can um
go from 30
that's 30.
um go from 35
across
and down from there
so
that comes out as
28 seconds so
this isn't the answer so that's what
we've been looking for and the answer is
28 seconds
the interquartile range so the upper
quartile and lower quartile
the median's half the data which was the
35th piece so the quarters
are
well so we're going to go
one quarter of 70
is half of this so 17.5
so
just underneath 18 um so we go just
underneath 18 to the line
and
down from there
which is
well 21 or 22 seconds so let's say
lower quartile
is
20
two seconds
upper quartile
so three quarters of 70 so that'd be
17.5 plus 35 that'll be 52.5 so just
above the 52.
and then from there
we go down
let's say that's in the middle
so that will be
39
so the upper quartile
39 seconds
so the interquartile range
39
take away 22 and that is 17 seconds
um usually you'll find that these
numbers are actually easier and it's
normally 80
so a quarter will be 20
um or a hundred quarterly 25 um they're
not usually 70. um estimate the number
of people
the number of people more than 42
minutes late so these were actually
minutes
let's change them to minutes um
so the number of people more than 42
minutes late
so we're looking at 42 minutes
which is here
go up to the curve
all the way along that line
and it comes out there
so it's coming out at
56.
so
56
um
is
well after 42 minutes 56 people have
arrived so
we're looking at the gap
here more than
so more than 42 it's this side
so
it's
how many more than 56 have we got 56
have arrived how many more have we got
so 14.
okay see if you can try this question
so first step to get a running total so
cumulative frequency and run in total
five as on the next one
keep heading on the next one
58
60 so a much nicer number this time
complete the graph plot the top points
top points against free cumulative
frequency so 10 against
five 20 against 15
30 against 35
40 against 50
50 and 58
and 60
60.
smooth curve to join them up
try and not miss the points like me
and then we're asked to find the median
so the median is a middle number if i've
got 60 on the frequency 60
and half of that the 30th so the 30th
one
along from 30
and down
so 28
28 minutes
interquartile range i mean the upper
quartile and the lower quarter
so
a quarter of 60 is 15 so we go along
from 15
and down so that was 20.
upper quartile that's 45
so
along from 45
and down so it's halfway in there
that's
37
so
37 interquartile range
37 take 20 which is 17 minutes
number of people more than 46 minutes
late so
we're looking at 46
on the minutes
up from there
meets there in the middle
and that's going to come out
at 55 people say 55 there was it more or
less than it was more than
so we want those people
which are those people
that's five people five people
you
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