MahritaHarahaputseduau Week 1 Tutorial Foundation Mathematics for Business Statistics The objective of this tutorial is for students to identify gaps in their maths knowledge early so they dont make errors and little mistakes that will cost them marks in other assessments ID: 779436
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Slide1
26134 Business Statistics
Mahrita.Harahap@uts.edu.auWeek 1 Tutorial: Foundation Mathematics for Business Statistics The objective of this tutorial is for students to identify gaps in their maths knowledge early so they don’t make errors and little mistakes that will cost them marks in other assessments. Please go through the PowerPoint file “Calculator”.
1
WHAT IS STATISTICS?
Slide2BSTATS-KEY ASSESSMENT ITEMS
2
“THRESHOLD CONCEPTS”
THRESHOLD
WEEK
THRESHOLD CONCEPT 1 (TH1): Identifying relevant data, understanding measurement properties of data
WEEK 1
THRESHOLD CONCEPT 2 (TH2): Understanding Data and summarizing data
WEEK
2
THRESHOLD CONCEPT 3 (TH3): Relating variables and analyzing relationships between variables
WEEKS 3-5
THRESHOLD CONCEPT 4 (TH4): Theoretical foundation of statistical inference-Understanding events and using data to calculate the probability of occurrence of an event.
WEEK 7
THRESHOLD CONCEPT 5 (TH5): Theoretical foundation of statistical inference: Collecting samples and drawing inference
WEEK 10
THRESHOLD CONCEPT 6 (TH6): Theoretical foundation of statistical inference: Building interval estimates and constructing hypothesis for statistical inference
WEEKS 11-12
Slide3THRESHOLD ASSESSMENT
3
TH 1
TH 5
TH 3
TH 4
TH 2
TH 6
WEEK 5
WEEK 9
WEEK
11
QUIZ 1
QUIZ 2
FINAL EXAM
“MAKE-UP QUIZ
MARKS
10 marks
10 marks
20 marks
10 marks
10 marks
20 marks
Assignment
20 marks
100 marks
= alternate opportunity to achieve marks for TH1 and TH2
= alternate opportunity to achieve marks for TH3 and TH4
Slide44
Slide5Student Resources
UPASS - is a voluntary “study session” where you will be studying the subject with other students in a group. It is led by a student who has previously achieved a distinction or high distinction in that subject, and who has a good WAM. You can sign up for U:PASS sessions in My Student Admin https://onestopadmin.uts.edu.au/. Note that sign up is not open until week 1, as it’s voluntary and only students who want to go should sign upTo Sign Up to these groups go to this website: helps-booking.uts.edu.auMaths Study Center @ CB04.03.331Free drop-in one on one consultation tutoring
on math/stats related questions 11am to 5pm on weekdaysOnline resources such as youtube or www.khanacademy.org Discussion Board on UTS Online
5
Mon
09:00-10:00
CB02.06.37
Mon
10:00-11:00
CB02.06.37
Mon
11:00-12:00CB02.06.37
Mon14:00-15:00CB02.06.37Mon16:00-17:00CB02.06.37Mon17:00-18:00CB02.06.37Tue18:00-19:00
CB02.06.37Wed09:00-10:00CB02.06.37Wed11:00-12:00CB05C.01.015Wed12:00-13:00CB05C.01.015Wed
15:00-16:00CB05C.02.054
Slide6Question 1: Order of mathematical operation
6
BIDMAS: Brackets, Indices, Division and Multiplication, Addition and Subtraction
NOTE: in b), when there is a divisor line, it instructs you to treat the quantity above the numerator as if it were enclosed in a parenthesis, and to treat the quantity below the numerator as if it were enclosed in yet another parenthesis.
Slide7Question 2: Converting Units of Measure
a) 12.5 hours + 43.2 minutes = b) 26km/h + 4 m/s =
7
NOTE: To turn hours into minutes, there are 60 minutes in an hour, so multiply 12.5 by 60 and you will get 12.5 hours in terms of minutes.
NOTE: There are 1000 meters in a kilometer. So multiply 26 by 1000 to give you 26km in terms of meters. There are 3600 seconds in an hour, so to turn m/h into m/s, divide 26000 by 3600 to give you 26000m/h in terms of m/s.
Slide8Question 3: Square Root
8
REMEMBER: (from q1) when there is a divisor line, it instructs you to treat the quantity above the numerator as if it were enclosed in a parenthesis, and to treat the quantity below the numerator as if it were enclosed in yet another parenthesis.
Slide9Question 4: Indices Rules
9
NOTE: in d), mathematicians define y
^0 = 1 in order to make the laws of exponents work even when the exponents can no longer be thought of as repeated multiplication. For example, (y^3)(y^5) = y^8 because you can add exponents. In the same way (y^0)(y^2)=y^2 by adding exponents. But that means that y^0 must be 1 because when you multiply y^2 by it, the result is y^2. Only y^0 = 1 makes sense here.
Question 5: Converting Decimals to Percentage to Fractions
10
NOTE: this is a very fundamental concept and often very handy to simplify and solve problems. From decimals to percentage, multiply by 100. From decimals to fractions, divide the decimal form by 1 then
multiply top and bottom of this fraction by the value that will give us an integer in the
numerator
.
(For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc
.). Then simplify the fraction.
Slide11Question 6: Mathematical Notation
11
Because superscripted exponents
like 10
7
cannot always be conveniently displayed, the letter
E
is
often used to represent "times ten raised to the power of" (which would be written as "× 10
n
") and is followed by the value of the exponent; in other words, for any two real numbers m and n, the usage of "mEn" would indicate a value of m × 10n.
Slide12Question 7: Factorial !
If n=10, p=5 , y=0, Find n!, p! and y! For the same values calculate p!/[(n-p)!]=
12
NOTE: To find out why 0!=1 go to http://mathforum.org/library/drmath/view/57128.html
Slide13Question 8: Exponential functions
13
On the calculator:
Slide14In statistics we usually want to statistically analyse a population but collecting data for the whole population is usually impractical, expensive and unavailable. That is why we collect samples from the population (
sampling
) and make inferences about the population parameters using the statistics of the sample (inferencing) with some level of accuracy (confidence level).
A
population
is a collection of all
possible individuals, objects, or measurements of interest. A
sample
is a
subset
of the population of interest.