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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