1

Chapter

deals with the tabular of data

Descriptive statistic or
graphical presentation

characteristics measured counted & Observed

variable refers to being ,

data from form to obtain frequency distribution table

Data Array is raw survey arranged in a table

statistical inference is
process of arriving at conclusions , predictions ,
forecasts or estimates based on data

Numerical Data Categorical Data

• Numbers •
Not numbers

Ex : no . Of cars owned F- × : what model of car owned

: How much do I
spend :
which brand of
shampoo

Discrete data continuous Data

measurements ( vary )
whole numbers
◦
•

limit
•

countable
•
got
✓ decimal
✗ decimal
•
•

•
Uncountable

Ex :
No . Of cars owned

what Ex Weight of
person
:
is shoe size : a

:
length of a stick

4 decimal
place / Whole
•
no .

2 decimal 1- unit
place
•

① data / data )
Ungrouped data ( can be discrete continuous

Ex : 1 3 I 9 7 ,
6 ,
3
, , ,
,

② data without
Grouped interval ( discrete data )

?
"° " "" "
±" "
"

"" ""

O 5

I 3

3 I

③ Grouped data with interval ( can be discrete data / continuous data )

f
"" " ☆ "+ "+" " ° " " ˢ
"
" "" ° ˢ
" "
° ^^ " "
° ° " & + ° "
"
"
"

+" "
'
" "

1
3- 4 2.5 4- 5
0 I
-

I - 2 5 5 -
6 4- 5 -
6. 5

2- 3 3
 standard bar graph

•
used to display data

class
^
no .
Of death title
^
A

2 -

' -

°
I
> Hurricane ° > NO . Of
4
'

A B C D i I 3 É Students

Bar
Component Chart

see how the make individual items

components up
•
sub -

no .
Of
tittle
employees
^

30 -

20 -
% Female

% male

10 -

> Departments
maintenance
Finance
Engi -

nearing

comparative Bar chart

•
to do for item
comparison each

$ tittle
^

300k -
% Total Revenue

% Total Expenses
% Profit / loss
200k -

100K -

o
> year
20 03 2004
 Line Graphs

track how variable

one
changes
•

show
comparison between two items time
•
over

no Of
.

cars tittle
^

*:X
• Honda

☐ myvi

> year
2000 2001 2002

Pie charts

Show how divided into

parts
•
whole amount is

composition

tittle

other
1. follow clockwise
20 / -

Nike 2 . start with

biggest sector

New 32%
Balance ☆ Find to find Angie
7115.2° percentage
23%
0.32 ✗ 360 =
115.2

Adidas
no need write angle ?
L
25 / .

Dot plot

of the of distribution
•

provides quick view

shape

tittle

• •

• •
p •

• •
• • •

>
-1020304050
 stem and leaf plot

•
Provides a quick view of the
shape of distribution

tittle
split stem -
leaves ( when -45K¥ #-)

I
6 0 8 8 24
' 2 3

7- 2 2 4 6 25 I 1 I 1 4 45 5 7 7

8 3 3

9 I o
tf

key : 5 / I =
51

24 I 2 3

24

25 I 1 1 I 4 4

25 5 7- 7
5

1 45 0 -
4

T
. 45 5 -
9

Histogram

data interval
group with
•

•
N -
axis = lower boundary

y-axis =
frequency
 Chapter 2

mean : arithmetic
average

median : centre value

mode :
highest occurrence or most
frequent data

data
Ungroupped

In median n -1 '
no mode
mode most
=
mean = : occur or

n 2

☆ mean
symbol is ñ

Grouped data without interval

It "
If -11
mean =
median =
mode :
highest frequency
2
If
↑
position
☆ is
midpoint
n

data with interval

Grouped
-
_

If
-

[ fn FB d
median mode
-
'
mean = = z =
+ ✗ a + ✗ c
It fm ditdz
- ,

☆ median class ☆ modal class

FB = Cf before median class d. =

diff of highest f and

fm tot median
the 1- on
top
class
=

da = diff Of highest f and

the f below

mode from from

Find
histogram Find median ◦
give
a- %
^ ^

i. 50%
1

,
1
I
!
I > >
↑
mode
median
 Chapter 3

MOD ← means of
dispersion
Range
IQR ( interquatile range )

standard deviation 0

Variance 02

Range
maximum value minimum value ( t )
provide rough measurement
ungrouped
-
=

diff of Max & min valve

C- ) only show

if range is not
highest data lowest data c- ) there's outlier accurate
grouped ✗ interval = -
,

NO Of
£
.

ex :
siblings
I 5
Range = 3- I

=
2
2 2

3 3

✓ interval OB LB
group
= -

F- × : Age f ( t ) ✗ affect by extreme values

information Of Q' 4 03
20-30 3
Range = 50 -
20 C- ) only can provide
'
30 -40 =
30

40-50 2

Interquatile Range

IQR = Q} -
Qi

Q, Qz 013

251 . 25-1 .
251 .
251 .

lungrouped data ) ( groupped ✓ interval )

- -

Q, =
n -1 '

¢
( Ntl ) ✗ 0.25 Q' =
¥- -
FB
+ ✗ C
fm
Qa =
ME
'
/ ( ntl ) ✗ 0.5
-

Qz =
3. ( ntl )
4
/ Intl ) ✗ 0.75
- -

Q2 4- -
FB
1,3
=

+ ✗ C
tm
( grouped data ✗ interval ) -

- -

Q, = ( If -11 ) ✗ 0.25
013 =
¥1T -
FB
+ ✗ C

( Et -11 ) fm
Qa = ✗ 0.5
-

Q} = ( If -11
) ✗ 0.75
 standard deviation

( grouped interval ) interval )

lungrouped ) ✗ ( grouped ✗

2 2

[④
2
"
I E.tn Efnz Itn
¥ ,

f-
n' It Et
o If It
o = o = =

↑ ↑ A- 4. ☐ 1- N2 7. TÉ ( fn )
≥

square }
- - ×

It -

EE

☆ n is class ☆ N is
midpoint

( MOD )
high measures of dispersion

further
spread of data

high variability

low consistency

lower reliability
 Box -

plot

5 no . Summary

→
min data

→ Qi

→ ①2

→ ①3

→ Max data

if it's outlier :

LB : Q - 1.5 ✗ IQR
,

UB : 013 1- 1.5 × IQR

• must have title

of skewness
chapter 4 : measures

1 . Symmetrical -
> normally distributed

2 .
Asymmetrical ( Skewed )

^
skewed Positively skewed
negatively
( skewed to left ) ( skewed to right )
^
✗

A. A .

" " "" " " """

"" " ""
"

, A A
• mean = median = mode • mean < median < mode • mode < median < mean

: the distribution is : the distribution is skewed : the distribution is skewed

approximately / reasonably to left where 75% of data to right where 75% Of data

symmetrical is between Qi to Max is between min and Q3

4- ☐ ¥
'
EE # ¥-7 -2g -
*¥ ,
☒ E

① 0.5 Hy → symmetrical

② > 0.5 → left / right

 5 normal distribution
Chapter :

I
1
I

'
1

I
1 99.71
I I
.

1 < 1
I ?
, 1 I 1 I
ñ -3s I -2s Tr -
S Je ñts ñtzs I -135

-3 -
2 - 1 I 2 3
2- Scores

Values

"

[ ]
"

☆ must use brackets follow by units

2- scores

n I
2 =
-

✗ Provided

¥
standard deviation

1 . if value is big it is far from mean

,
more unusual ( less likely to
happen ]
,

2 .
if value is small ,
it is closer to mean , less unusual ( more likely to happen )

☆ Virtually ( 99.7% )

two third ( 68-1 )

.
 Chapter 6 :
Probability of an event

(E) of even -1 A can occur

PCE ) = n ← no . ways

HIS )

↑
total no . Of possibilities outcomes

Probability : measure of how likely an event is

of
event
:
one or more outcomes an
experiment

outcome : result of a single trial of an experiment

experiment : situation involving chance or

probability
that leads to results

Types of event

mutually exclusive → both events

i. cannot
happen at the same time

F- × → toss a coin ( heads and tails cannot at the same time )

→ which the time

2 . Non mutually exclusive events can occur at same

F- → '
6
'
)
×
Toss a die ( even no . and a

events event does not the other

3 .

Independent → occurrence of one affect

F- × → choosing breakfast ✗ affect where

you sit

4 . Dependent events / → outcome of one event is dependent on another event

conditional probability
event Ex
→
being able to drive
depend on starting car

5. event → either occurs does not

complementary occurs
or

Ex → PCA ) -1 PCE ) =L

choose not
coffee or
choosing coffee

dice
Experiment 12011 a

Outcome / sample space s= { 1,2 ,

3 ,
4 , 5
,
6 }

event even no = { 2
,
+ ,
6 }

complementary events : if an event is A then complementary event is not A

P( A) + P (F) = I
 7 Probability
Chapter Sample
:
space
-

1 Grids
Lists or

Grids of total Grids of Pairs

I 2 3 4 5 6 I 2 3 4 5 6

1
I 2 3 4 S 6 7 11 12 13 14 15 16

2 3 4 5 6 7 8 2
21
④④ 24 ④ 26

3 4 5 6 F 8 9 3 31
④ ④ 34 ⑤ 36

4 5 6 7 8 9 10 4 41 42 43 44 45 46

S 6 7 8 9 10 11 5 51
⑤ ⑤ 54 56

6 7 8 9 10 It 12 6 61 62 63 64 65 66

FE intersection

PC pair of prime
hunters ) =
% =
¥

☆ is
probability of each outcome
equally likely

2 Venn Diagram

} : universal set

'
'

n :
intersection ( =
. / and

' '

U
: Union ( ) or

'

A / it :
complement ( )

A •

C :
Subset ( ,

∅ :
empty set

} } A
f) B
A
Only
B
A
AMB Only B
only ANB
C
Anc

ANBNC

B
C
Only B"

Only
 3 Tree Diagram

( with replacement )

Red ball
}
:
5
7- balls
Blue ball : 2

¥ Red
if red red =
¥ ✗ ¥
¥ Red
Blue
=

¥9
¥
BOX
¥ Red

¥ Blue

blue
¥

( without replacement )

}
2
strawberry 7 candy
5
mango

I s
if strawberry mango
¥ s
m
¥ %
§ = ✗

BOX ¥
s
=
¥2
¥ m

¥ m

④ 2 way table

'
A A Total

B AMB AMB total B

A' AB
' '

B
'
ANB total B
'

total A
'
total A total
Total
everything
 8 :
Probability Laws
Chapter

: P( A) + PCE ) = 1
law
complementary

PC AUB ) = PCA ) -1 PCB ) PCANB )

Addition Law
-

conditional probability law :

PCA / B) = PCANB )
↑ PCB )
given
that