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A Level Statistics notes Edexcel

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All of Statistics in A level are covered in this document, with detailed walk-throughs on example questions from an A* in A Level Maths student.

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  • October 17, 2021
  • 16
  • 2020/2021
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Doobeans
Statistics

Population the whole set of items that of interest



is are .




A observes of
member
population




census or measures
every a .




A subset of intended
sample is some the
population to represent the
population


.




CENSUS SAMPLE

Advantages Advantages
: :




↳ result
gives a
completely accurate .
↳ Less time
consuming
&
expensive than census



↳ Fewer
people have to
respond

Disadvantages :
↳ Less data to
process
than in a census



↳ Time &
consuming expensive


Disadvantages
cannot be used if the
testing

process :




destroys the item ↳ data not as accurate

↳ of
hard to
process large quantity data ↳
sample may not be
large enough to
give
information about small sub of the
groups
-




Sampling units are individual units of a
population .



population .




Sampling frame is a numbered list of
sampling
units of a
population .




Random number
generator using calculator '

-




g.
min *

,

Menu 8 OPTION 2 Value Ran Int Cl too )
SAMPLING

OF
→ → →
TYPES
:

,


t how
many
d
to be


RANDOM SAMPLING Range :
A1 :
A 20 chosen




1) SIMPLE RANDOM SAMPLING 2) SYSTEMATIC SAMPLING 3) STRATIFIED SAMPLING

where item frame divided into strata s and
sampling population
-



in elements chosen at
.




required
a
every
a


are



of
has an
equal chance
being chosen .




regular intervals from an ordered list .

simple random
sampling is carried out

stratum
stamp 's
no in
each item has
identifying number ( ) starting overall


on
Take Kth item K
'




in each
-
.




group
-




every
.

×

sample
.



size
' '
no ,
in population
lottery sampling
Use random number
generator at random item between 1 and K
proportion sampled from each
• .



same
group
. .
.




Adv bias free Adv and Adv reflects
population structure
quick
:
simple
- : :




&
cheap suitable for
large populations guarantees proportional representation
:

easy
: :
.




not suitable for Dis frame needed of
Dis
large population sampling
within
population
:

groups
: .




frame needed Dis
sampling introduce bias if population must be
clearly
:
classified
sampling
: .
:
can into


each stratum
( dis
+ within
)
,




frame not random distinct strata . adv .
of
simple random

,•
NON RANDOM SAMPLING -




1) QUOTA SAMPLING 2) OPPORTUNITY SAMPLING

Population divided into
according sample taken from
people who
present at




are





groups

to characteristic meet criteria
.
time of
study ,
who


Adv to out
easy carry
:

A
quota of items in each set



is
group

to reflect the
:
inexpensive
try and
group
's
proportion
Dis to representative sample
unlikely provide
:
a
in the whole
population .




highly dependent individual researcher
:
* on .




Interviewer selects the actual units
sampling



.




Adv .
:
allows small sample to still be representative

of
population .




sampling frame
required
:
no




quick
:
,
easy , inexpensive

:
between
easy comparison groups
Dis random bias
non
sampling can introduce
: -
.




divided into be
costly / inaccurate
groups can
:
;


of number of
increasing study increases
i.

scope

time d
groups , adding expense .




Northern hemisphere :
Jacksonville

Beijing


Southern hemisphere : Perth



Typical
:

ranges


* + r / trace < " 05mm
Mean rainfall 1mm ) Maximum lkn )
treat as 0 gust
Mean 1°C ) Mean cloud ( oktas )
temperature cover



Total sunshine ( hrs )
*
to nearest to ( )
Daily mean
visibility Dm

hecto pascals
( knot / Beaufort scale )
Daily mean wind
speed Daily mean
pressure
1hPa )
↳ 0 =
calm

I kn 1.15
↳ I -
3 =
light
=

mph ( %)



4

5
=



=
moderate
fresh
Daily maximum relative
humidity

, MEASURES OF LOCATION AND SPREAD
'"
( )
CUMULATIVE FREQUENCY

Mean : I =
n
discrete


[ set
n
I =
sf ( grouped )

80



§
3


/
on
if whole number between this
IT
take
halfway q
)

Lower quartile Q i

.
,


above
, ,
and the one .


• 60 -




if not whole number, round
up
and take this E





Upper quartile Q, :
Zan
data point 40
,
.

g
E

E
" median

Using interpolation
:


o >

h ( )
↳ to estimate median g, Height mm


quartiles percentiles
,
mean
, , ,




*
distributed
Assumption : data values are
evenly within each class .




↳ median falls in the class
3kg Ex <
7kg C O D l N Cy
e.g .




" "

3kg 7kg If the data coded the formula =
I
is
using y g

7
' t 21 ⇐ cumulative I -
a

the of the coded data
g-




frequency mean is b
=



original O



[Y

× (
7kg 3kg ) -



) t
3kg
=


5.86kg standard deviation of coded data
O, not affected


Oy
"

, by the
'
=
the a
.

is b
-




*
remember for continuous data been
:
,
values
might have




rounded
up
1 down .
OUTLIERS
( 3ms " E 5M include values from 2. son to 5. Sm ) ↳
an extreme value that lies outside the overall
pattern
may

of the data


Variance
'

( O ) mean

d
,

IT
'




{( Ssi I S×× the data
'


x
Cleaning is the
process
of
removing
-




= -
=

n n n n

anomalies from the data .




'




Sxx =
{(x -
x-p =
q , ,z -
Knx )

Standard Deviation BOX PLOTS
Q median
-




" "


)
Ibn
{
In Sn Snxx
' ,
-
I " "
"
O = = -

= ← Qs
outlier

X


T r
lowest value that value that
highest
For
grouped frequency calculate estimates of is not an outlier is not an outlier
,
l l l l l l l


' O 80
G and of each class interval
using midpoints
O .




Using the calculator :




Menu → 6 → 1 -
Variable →
input values → OPTION → 1 -
Variable calc



Frequency :
setup → down → statistics → on

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