01
Phân tích môi trường ngành
03
Môi trường vĩ mô
02
Cơ hội và nguy cơ của doanh
nghiệp
understand how to use fraction and
percentages
05
Round numbers up or down
07
04
Caculte three kinds of average and
five-number spreads
06
Understand the basics of interpreting
data in gaphs, tables and charts
Môi trường vĩ mô
1.
2.
3.
4.
5.
6.
Môi trường kinh tế
Môi trường công nghệ
Môi trường văn hóa xã hội
Môi trường tự nhiên
Môi trường chính phủ
Môi trường toàn cầu
Build confidence with numbers
Obstacle of student :
 Anxiety
 Stay calm
 Don’t rush
 Practise
Land of mathematical
enlightenment
Specialist workshop
More practice
Computer packages
Practice
Workshop&
classes&advice
Asking for help
Calculators
Willingness to have a go
Don’t
understand
numbers at all
Caculating
averages and
percentage
Too many little
mistakes
Overcoming
barriers
Can’t track
numbers
Multiplication
and division
Quickly forget
• How useful are numbers?
• What are statistics?
• The relevance of numbers
Understand how to use fractions
and percentages
The language of
fractions
-Straightforward
One- eighth
Two-eighths
Written fractions
The top number
or numerator
The lower number
or denominator
Fractions of a set
7 equal parts: ⅟7 of 28
items is 4 items
3/7 of 28 items is
3*4 items = 12 items
•
•
•
•
•
•
•
1
2
3
4
5
6
7
Proper and improper fractions
Comparing equivalent fractions
• The height of each column
• The items in each column
Comparing fractions
• The same bottom number (denominator)
𝟐 𝟒
<
𝟓 𝟓
𝟕 𝟓
>
𝟖 𝟖
•The bottom number differ
1
𝟏
𝟒
or
>
𝟐
𝟗
*For 4 : to get 36 at the bottom, you multiply 4 by 9, so
9
1
multiply the top, 1, by 9 also. The result is 36 (that is: 4 =
2
9
).
36
*For 9 : to get 36 at the bottom, you multiply 9 by 4, so multiply
8
the top, 2, by 4 also. The result is 36 ( that is
2
9
8
= 36).
Adding and subtracting fractions
• Once you have converted number so that they
have a common denominator, you can also
add and subtract fractions easily. You simply
add or subtract the top number:
•
•
9
+
36
5
+
36
8
17
=
36
36
11
16
=
36
36
9
8
−
36
36
30
10
−
36
36
=
=
1
36
20
36
Using fractions
Use of fractions
We use fractions in
everyday life:
• To share any items in
equal parts
• To share out profit in
proportion to the level
of investment
• To work out a sale price
when items are
reduced by a fraction,
1
such as ‘ 𝑜𝑓𝑓′
3
Calculating the fraction of quantity
For example, if we know that in a
survey of 800 people, three-quarters
were women, we can work out how
many women were questioned.
3
In 800 participants, were women.
4
1. Divide the total number by the
bottom number in the fraction:
800
= 200
4
2. Multiply the result by the top
number in the fraction:
200 x 3 = 600
Using fractions
Multiplying fractions
When you multiply fractions of
a whole number you are
multiplying a part by a part, so
the result is even smaller. For
example:
-
A half of a half
quarter
-
1
( )
4
1
(
2
x
1
)is
2
1
2
1
8
a
A half of an eight ( x ) is a
1
16
sixteenth ( ).
Top-heavy fractions
Sometimes you see a fraction in
which the top number is bigger
than the bottom number. This
simply means that fraction
amounts to more than one whole
11
item or set. For example,
is the
same as
6 5
+
6 6
or
5
1 .
6
6
Understanding percentages
A proportion of the ‘whole’
The whole of anything- the full amount
of an item or a group of items – is 100%.
If some of the cake is eaten, the
remainder can be expressed as
percentage of the original whole cake
Percentages written as
fractions
1
100
23
100
59
100
= 1% (1 per cent)
= 23% (23 per cent)
= 59% (59 percent)
Percentages: ‘more than one cake’
Calculating percentages from fractions
Converting fractions to
percentages
1 Divide the part by the whole.
2 Multiply the result by a 100.
Example
17/34 = 0.5
(17= ‘the part’; 34 = ‘the whole’)
0.5 x 100% = 50%
Rounding up and down
• Whole numbers
A whole number is one with no fractions or
decimal points attached to it, such as 75 or 921
• Numbers followed by decimal points
Decimal
point
Whole number
Part of a number, amounting to less
than the number one
23.627197
First
decimal
place
(tenths)
Second
decimal place
(hundredths)
Third decimal
place
(thounsandths)
Sixth decimal
place
(millionths)
Rounding up and down
Rounding numbers
Example: Rounding down 986.748
• The digit in the first decimal place is 7.
• The digit in the next decimal place is a 4, so round down,
removing the 4 and the 8, and leaving 986.7.
Example: Rounding up 986.752
• The digit in the first decimal place is again 7.
• The digit in the next decimal place is 5, so you round up,
removing the 5 and the 2, changing the 7 to 8, and leaving
986.8.
What are ‘averages’ ?
Calculating averages
: The mean
1
6
5
2
Calculating
averages : The
median
Five
number
summaries
and
quartiles
3
4
Comparing means,
median and modes
Calculating
averages : The
mode
Averages:
The
median
The mean
The mode
 The mean
What is the mean?
The averages
=
The mean
Calculating the mean :
 Add up all the numbers
in the set in order to
find the grand total , or
‘sum’ of the numbers.
 Divide the sum by the
number of items in the
set: that gives you the
mean average.
Data
set
2 , 4, 6, 8, 3, 1
Example
Different
numbers
Example
1:
2, 4 , 6, 8,
3, 1
2+4+6+8+3+
1= 24 Six numbers
24
=4
6
MEAN : 4
Different
heights
The Median
What is the
median?
Calculating the
median:
The mid-way point in
a set of number .
 Lay out the number in
the set in order from
smallest to largest.
When is the
median useful ?
The median is
especially useful for
small sets of
numbers.
 The median is the
middle value
 The way of calculating
this place depends on
whether there is an
Example 1 : Odd number
of items
Here is set of exam scores
Median 7
5 , 10 , 3 , 7, 6 , 2 , 4
Example 2 : Even number
of items
Here is another set of
exam scores :
7 , 6, 10 , 8, 2, 5 , 4, 1
.
8 + 2 = 10
10
⇒ =5
2
Median : 5
The mode
What is the mode?
The number in a set
that appears the most
frequently
When is the mode
useful?
When you have a large set of
data in which there is only a
small range of values.
 Example1:
Look again at this of exam scores ,
sorted into ascending order:
59,59,
59
23,36,42,56,57,58,59,59,59,69,99.
The mode is 59
 Comparing means , median
and modes
Find the mean, median, and
mode of the following set of
numbers :
1, 9 , 4 ,10 , 4 , 8.
1+4+4+8+9+10
 Mean :
6
=6
1 , 4, 4, 8, 9, 10
4+8
⇒
=6
2
 Mode : 4
 Median :
Five-number summaries and
quartiles
Maximum
number
Minimum
number
Median
Lower
quartile
(LQ)
using five-number summaries
Using tables, charts and graphs
Find visual Information
See relationships
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Why do we use line
graph ?
6
How do you plot a grahp ?
5
4
Series 1
3
Series 2
2
Series 3
1
0
Category 1 Category 2 Category 3 Category 4
-Are table better more than -graph
-what is the difference between table and
chart graph