Technology 8.1 The Calculator
Scientific calculators will calculate descriptive statistics such as mean and sum.
1 Change the calculator mode to Stat or SD 2 Clear the calculator.
2 Enter a number then press M+
3 Repeat entering a number and then pressing M+
4 Find the x button, this is the mean.
5 Find the ∑x button, this is the sum of the numbers.
Technology 8.2 The Spreadsheet
Most spreadsheets will calculate a massive number of descriptive statistics and draw a frequency polygon:
1 Enter a set of data into the spreadsheet.
2 Enter formulas for the mean, median, and mode.
Technology 8.3 The Graphics calculator
A graphics calculator will automatically calculate a large number of descriptive statistics and draw a frequency column graph:
1 Select the STAT menu, EDIT, and enter data into one of the lists.
2 Return to the main screen.
3 Select the STAT menu, Calc, 1_Stats and enter L1.
To draw a frequency column graph:
1 Enter the numbers in L1 and the frequency in L2.
2 Use STATPLOT to set up the graph Xlist= L1 and Frequency = L2.
3 Use Zoom and ZooMSTAT to fit the graph if necessary.
4 TRACE.
Check your calculator's manual for Statistical calculations
Exercise 8.14
1 Join these four triangles together to make one large triangle.
2 How many integers between 1 and 100
have the sum of their digits equal to 10 (82 is one such integer)?
3 The numbers from 1 to 20 are put in a box. What is the probability of selecting a prime number from the box?
4 What are the next three numbers in the sequence: 1, 3, 6, 10, … 5 Five positive integers have their mode,
median, and mean all exactly equal to 2.
What are the five numbers?
6 By moving just three coins, turn the triangle of coins upside down.
The Tower of Hanoi is a game played by one person. The aim of the game is to move the three disks from the left peg to the right peg. The game can be played with different sized coins.
1 Only one disk can be moved at a time.
2 A larger disk must never be above a smaller disk
Ask for a number 1 Double the number 2 Add 6
3 Divide by 2
4 Subtract the original number The answer is 3
What about this trick?
1 Double the number 2 Add 10
3 Divide by 2
4 Subtract the original number
A Couple of Puzzles
A Game
A Sweet Trick
Can you do it in 7 moves?
Do you want to try 4 disks?
You will hear more about this well-known puzzle.
There are many Tower of Hanoi Applets on the Internet. Try one of them.
= (2x + 6)÷2 − x
= x + 3 − x
= 3No matter what number you give me, the answer will be 3.
Chapter Review 1
Exercise 8.15
1 What is wrong with each of the following:
a) 15 classmates were asked if they intended going to the social. 9 said yes.
The conclusion was that 60% of the school's population would go to the social.
b) Survey forms, asking about what music should be played at the upcoming school dance, were placed in the library along with the response box.
2 Find the range, mean, median, and mode of each of the following data sets:
a) 5, 2, 3, 4, 5, 4, 3, 4 b) 6.5, 6.5, 6.5, 6.6, 6.8, 6.7, 6.5 3 Which central measure, mean, mode, or median would be most useful in each of
the following cases?
a) The average height of Year 8 students
b) The average number of animals in each family c) The average wage
4 Draw a frequency column graph for each of the following surveys after first constructing a frequency table:
a) A coin was thrown 38 times:
H H T T H T H T T T H H T H T H T H H T T T T H H T T H H T T H H T T H T H
b) A survey on whether mobile phones are a classroom distraction:
Disagree Strongly agree Agree Disagree Disagree Disagree Agree Agree Disagree Disagree
Disagree Agree Agree Agree Disagree
Agree Disagree Disagree Disagree Agree
Agree Disagree Disagree Disagree Strongly disagree 5 Suspecting that there were different distributions of students in form groups, year level data was taken from two form groups. Analyse the data and make a comment.
Red form Blue form
7 8 8 12 9 9
10 12 11 7 8 10 11 8 12 11 12 7
7 7 8 7 12 8 9 8 10 11
8 7 10 8 10 10 9 11 10 10 12 11 11 9 7 7 8 7 11 12 10 12 11 12
7 10 10 12 8 10
6 A person has an average of 80 after four tests. What mark must the person get on the fifth test so that the average of the five tests is 85?
Chapter Review 2
Exercise 8.15
1 What is wrong with each of the following:
a) 5 Year 7s, 5 Year 8s, 5 Year 9s, 5 Year 10s, were asked about their study habits. The conclusion was that between 30% and 80% of students study for less that 2 hours per night.
b) Survey forms, asking about what music should be played at the upcoming school dance, were placed in the library along with the response box.
2 Find the range, mean, median, and mode of each of the following data sets:
a) 3, 4, 3, 2, 5, 2, 3, 5 b) 1.2, 1.4, 1.1, 1.3, 1.3, 1.2, 1.2 3 Which central measure, mean, mode, or median would be most useful in each of
the following cases?
a) The average weight of Year 8 students.
b) The most popular shoe size.
c) The average house price.
4 Draw a frequency column graph for each of the following surveys after first constructing a frequency table:
a) A die was thrown 36 times:
5 2 1 5 6 5 1 3 4 1 6 2 6 6 5 3 2 6 5 4 4 1 6 1 3 3 3 1 6 3 2 4 3 2 1 4
b) A survey on whether rubbish in the schoolgrounds is a problem:
Disagree Strongly agree Agree Disagree Disagree Strongly disagree Agree Disagree Disagree Disagree
Agree Disagree Disagree Agree Agree
Disagree Strongly agree Agree Disagree Disagree Agree Disagree Strongly agree
5 Suspecting that drivers were more careless with their car speed on public holidays, radar gun readings rounded to the nearest 5 km/h, were taken in a 50 km/h zone were taken on a normal workday and the public holiday the next day.
Analyse the data and make a comment.
Workday Public holiday
50 40 50 45 45 50 50 40 40 35 45 40 50 50 55 60 70 55 50 40 40 55 45 45 50 60 70 55 50 50
50 55 50 50 50 65 50 55 60 50 40 50 55 50 40 65 70 50 55 50 60 50 55 50 50 55 45 50 55 50 6 A person has an average of 45 after four tests. What mark must the person get
on the fifth test so that the average of the five tests is 50?
A TASK
π
is a very important mathematical and physical constant and is often used in engineering, science and mathematics.y Research the history of π.
y π is irrational. What does this mean?
y Design an experiment to calculate π.
y Report your findings (poster, oral report, etc.).
A LITTLE BIT OF HISTORY
The Ahmes Papyrus is about 6 m long and 35 cm wide. It was a copy, made around 1650 BC, of a 200 year old version.
The Papyrus contains 87 mathematical problems.
The Papyrus has a formula for the area of a circle:
This is the same as: Area= 25681r2 Thus their π = 3.16
Investigate the relationship between features of circles such as circumference, area, radius and diameter.
Use formulas to solve problems involving circumference and area.
Investigate the circumference and area of circles with materials or by measuring, to establish an understanding of formulas.
Investigate the area of circles using a square grid or by rearranging a circle divided into sectors.
Area= 64d 81
2
Hi I'm Pi.
My name rhymes with hi and bye.
What is the relationship between the circumference and the diameter?
Exercise 9.1
1 Get some circles
(e.g., drink cans, coins, toilet rolls, pipe).
2 Measure the diameter.
3 Measure the circumference.
4 Calculate the ratio
Object Diameter (d) Circumference (C) C ÷ d Jar of curry paste
Drink can 6.5 cm 21.2 cm 21.2 ÷ 6.5 = 3.26