Assessment Task A – Assessment Task A – Learning ObjectLearning Object

RELATIVE FREQUENCYRELATIVE FREQUENCY

By Staceylee, Courtney & HeatherBy Staceylee, Courtney & Heather

Today's Lesson Includes;Today's Lesson Includes;

• Introduction of topic - What is relative frequency?Introduction of topic - What is relative frequency?

• Worked ExampleWorked Example

• Introduce Learning ObjectIntroduce Learning Object

• Real Life Contexts Real Life Contexts

• 3 Digital Resources Explained & Evaluated using PMI 3 Digital Resources Explained & Evaluated using PMI (Plus Minus Interesting)(Plus Minus Interesting)

• Wrap Up Questions Wrap Up Questions

Relative FrequencyRelative FrequencyWhat is Relative Frequency? What is Relative Frequency? (Experimental Probability)(Experimental Probability)

• Probability based on an experiment which is Probability based on an experiment which is written as a ratio (or fraction) comparing the written as a ratio (or fraction) comparing the number of times an event occurred to the number of times an event occurred to the number of trials.number of trials.

Relative Frequency formula Relative Frequency formula Relative Frequency = Relative Frequency = number of times an event number of times an event

occurredoccurred Number of trials Number of trials

When you gather data by observing a When you gather data by observing a random event, you can calculate the random event, you can calculate the Relative Frequency (experimental Relative Frequency (experimental probability). probability).

In order to calculate the relative In order to calculate the relative frequency of a random event, you use frequency of a random event, you use the following rule/ formula:the following rule/ formula:

(event) is the event(event) is the event

P (event) = P (event) = number of times an event number of times an event occursoccurs number of trials number of trials

where P is the probabilitywhere P is the probability

Another way to write Another way to write the rule for relative the rule for relative frequency is;frequency is;

Relative Frequency = Relative Frequency = ff

∑ ∑ff

Declarative and Procedural Declarative and Procedural Knowledge Knowledge

Declarative Knowledge Procedural Knowledge

Decimal Fractions Analyse data to identify the key mathematical content in the generation of an equation

Percentages Use mathematical interpretation and conclusions to generalise reasoning and make inferences

Probability Calculate relative frequencies from given or collected data to estimate probabilities

Frequency tables Substitute variables into formulas to determine an unknown

Relative frequency formula Select appropriate data from the information given

Terminology Investigate real life examples that demonstrate the use of relative frequency

Data interpretation Evaluate the appropriateness of sampling methods and sample size

Algebra – Variables and constants are represented using words and symbols when writing expressions and equations

EXAMPLE 1EXAMPLE 1

A student flipped a coin 50 times. The coin landed on A student flipped a coin 50 times. The coin landed on HEADS 28 times. Find the relative frequency HEADS 28 times. Find the relative frequency (experimental probability) of having the coin land on (experimental probability) of having the coin land on HEADS. HEADS.

Think Think

Write the number of times Write the number of times the coin landed on HEADS the coin landed on HEADS and the total number of coin and the total number of coin flipsflips

Write the rule for relative Write the rule for relative frequency (experimental frequency (experimental probability)probability)

Substitute the known values Substitute the known values into the rule into the rule

Answer the question Answer the question

Write Write

Number of times coin landed on HEADS = Number of times coin landed on HEADS = 2828Total number of coin flips = 50 Total number of coin flips = 50

P(event) = P(event) = number of times the event number of times the event occurredoccurred Total number of trials Total number of trials

P(HEADS) = P(HEADS) = 2828 5050

The experimental probability of the coin The experimental probability of the coin landing on HEADS is landing on HEADS is 2828 = 0.56 = 56% = 0.56 = 56% 5050

Marble ManiaMarble ManiaLearning Object. Learning Object.

50 Marbles 50 Marbles

Real life Contexts Real life Contexts •Apart from gambling, (mention Las Vegas) the Apart from gambling, (mention Las Vegas) the theory of probability can help us make relatively theory of probability can help us make relatively reasonable choices in our daily lives.reasonable choices in our daily lives.

•Students choose college courses which have a Students choose college courses which have a high probability of leading to employment after high probability of leading to employment after college.college.

•Many people have left New Orleans for good Many people have left New Orleans for good because there is a high probability of devastating because there is a high probability of devastating hurricanes in that region.hurricanes in that region.

•People don’t smoke because there is a high People don’t smoke because there is a high probability of their developing cancer as a result probability of their developing cancer as a result of smoking.of smoking.

Real Life Context cont.Real Life Context cont.•Probability has widespread use in business, Probability has widespread use in business, science and industry. Its uses range from science and industry. Its uses range from the determination of life insurance the determination of life insurance premiums premiums

•Sporting uses - in tennis the player knows Sporting uses - in tennis the player knows his relative frequency of wins in relation to his relative frequency of wins in relation to whether he serves or receives first.whether he serves or receives first.

•In cricket teams know the relative In cricket teams know the relative frequency of wins in relation to the pitch frequency of wins in relation to the pitch conditionsconditions

Digital Resource 1 WebsitesDigital Resource 1 Websites

• Experimental Probability Digital Resource - Experimental Probability Digital Resource - Joseph L. Coffman (2010) Joseph L. Coffman (2010) http://www.jcoffman.com/Algebra2/ch1_6.htmhttp://www.jcoffman.com/Algebra2/ch1_6.htm

• Relative Frequency Quiz – Lesson 6 Quiz - Relative Frequency Quiz – Lesson 6 Quiz - Pearson Prentice Hall Mathematics: Prentice Pearson Prentice Hall Mathematics: Prentice Hall’s online practice test (enter this web code Hall’s online practice test (enter this web code to play: aga – 0106) to play: aga – 0106) http://www.phschool.com/webcodes10/index.chttp://www.phschool.com/webcodes10/index.cfm?fm?wcprefix=aga&wcsuffix=0106&area=view&xwcprefix=aga&wcsuffix=0106&area=view&x=8&y=10=8&y=10

PLUS,MINUS,INTERESTING PLUS,MINUS,INTERESTING (PMI) on Digital Resource 1(PMI) on Digital Resource 1

PLUSPLUS MINUSMINUS INTERESTINGINTERESTING

Offers a great Offers a great definition on what definition on what relative frequency relative frequency (experimental (experimental probability) isprobability) is

Offers an easy to Offers an easy to follow example follow example (procedural (procedural knowledge) on correct knowledge) on correct rules and correct rules and correct setting outsetting out

Has a quiz which opens Has a quiz which opens in a new tab to allow in a new tab to allow you to test your skills you to test your skills and declarative and declarative knowledge knowledge

It is named It is named experimental experimental probability probability –– not not relative frequency relative frequency

Only offers one easy Only offers one easy example example

It offers an online quiz It offers an online quiz to test your knowledge to test your knowledge on relative frequency on relative frequency (experimental (experimental probability) probability)

http://www.zweigmedia.com/RealWorld/tutorialsf15e/frames6_2.htmlhttp://www.zweigmedia.com/RealWorld/tutorialsf15e/frames6_2.html

Digital Resource 2Digital Resource 2

Digital Resource 2 Digital Resource 2 Plus Minus Interesting

Meets most of the DK and PK neededCalculate relative frequency from given or collected data

Doesn’t use real life contexts

Quiz page. Need certain points to go onto the next one. You get a smiley face when you get it right!

Simple definitions, with examples

Not many questions

Gives you plenty of practice questions where you can help check you are on the right track before you put your answer in.

Digital Resource 3Digital Resource 3

Digital Digital

Resource Resource

33

Digital Resource 3Digital Resource 3

Digital Resource 3 Digital Resource 3 Plus Minus Interesting

It shows the DK needed for relative frequency : data tabulation; influence of sample size; formula for relative frequency

It is too simple It leads well from one topic to another

It is easily understood

It gives examples and explanations

For more info go to...For more info go to...

https://usingrealativefrequenhttps://usingrealativefrequency.wikispaces.com/cy.wikispaces.com/

Staceylee CourtneyHeather