Making PredictionsMaking Predictions

Using Ratios to Predict Using Ratios to Predict OutcomesOutcomes

What is a prediction?What is a prediction?

A prediction is a statement that describes A prediction is a statement that describes something that is likely to happen in the something that is likely to happen in the future.future.

What are some examples of predictions What are some examples of predictions you have heard people make?you have heard people make?

What did these people base their What did these people base their predictions on?predictions on?

When and why might you want to make a When and why might you want to make a prediction?prediction?

Using surveys and samplesUsing surveys and samples

A A surveysurvey is a method of collecting is a method of collecting information. The most common types of information. The most common types of surveys are interviews, telephone surveys are interviews, telephone surveys, or mailed surveys.surveys, or mailed surveys.

The group being surveyed is called the The group being surveyed is called the populationpopulation..

The entire group ofThe entire group ofstudents in a school is students in a school is an example of a an example of a populationpopulation..

To save time and money when the To save time and money when the population is very large, part of the population is very large, part of the group, called a group, called a samplesample, is surveyed., is surveyed. The group of students in one classroom The group of students in one classroom

is a is a samplesample of the population. of the population.

A A goodgood sample is: sample is: Selected at randomSelected at random Representative of the populationRepresentative of the population Large enough to provide accurate dataLarge enough to provide accurate data

A good sample is selected at A good sample is selected at randomrandom, or without , or without

preference,preference,Which method would more likely Which method would more likely

produce a produce a randomrandom sampling if sampling if surveying a large group about their surveying a large group about their favorite sport?favorite sport?

-Ask the first 25 students to enter the -Ask the first 25 students to enter the buildingbuilding

-Ask the first 25 students attending a -Ask the first 25 students attending a basketball gamebasketball game

A A goodgood sample is sample is representativerepresentative

of the population.of the population.Which method would more likely produce Which method would more likely produce

a a goodgood sampling if surveying a large sampling if surveying a large group about their favorite sport?group about their favorite sport?

- a class of students enrolled in athletics- a class of students enrolled in athletics

- A class of students enrolled in Social - A class of students enrolled in Social StudiesStudies

A A goodgood sample is large enough sample is large enough to provide accurate datato provide accurate data

Which method would more likely Which method would more likely produce a produce a goodgood sampling if sampling if surveying a large group about their surveying a large group about their favorite sport?favorite sport?

- A group of students in a classroom- A group of students in a classroom

- A group of students at a lunch table- A group of students at a lunch table

Using results to predictUsing results to predict

The responses of a good sample are The responses of a good sample are proportionalproportional to the responses of the to the responses of the population. population.

So, you can use the results of a So, you can use the results of a survey or past actions to predict the survey or past actions to predict the future results or actions of a larger future results or actions of a larger group.group.

Writing and solving a proportion will Writing and solving a proportion will yield a prediction.yield a prediction.

Example…Example… Lorenzo asked Lorenzo asked

every tenth every tenth student who student who walked into school walked into school to name his or her to name his or her favorite pizza favorite pizza topping.topping.

He recorded their He recorded their choices as shown choices as shown in the table.in the table.

Favorite Pizza Favorite Pizza ToppingsToppings

ToppingTopping StudentsStudents

pepperonpepperonii

1717

cheese cheese 88

sausagesausage 33

mushroomushroomm

44

If there are 320 students at his If there are 320 students at his school, predict how many students school, predict how many students prefer pepperoni pizza.prefer pepperoni pizza.

Step 1: Calculate the probability that a student Step 1: Calculate the probability that a student (from his (from his samplesample) preferred pepperoni.) preferred pepperoni.

Favorite Pizza Favorite Pizza ToppingsToppings

ToppingTopping StudentsStudents

pepperonipepperoni 1717

cheese cheese 88

sausagesausage 44

mushroomushroomm

33

P(pepperoni) =1177

3322

Let Let ss represent the number of students represent the number of students in the school ( the in the school ( the populationpopulation) who ) who prefer pepperoni.prefer pepperoni.

Step 2: Write a proportion. Step 2: Write a proportion.

Step 3: Solve the proportion. Step 3: Solve the proportion. Since 32 time 10 equals 320, Since 32 time 10 equals 320, multiply 17 by 10 to find multiply 17 by 10 to find s.s.

Of the 320 students, about 170 Of the 320 students, about 170 will prefer pepperoni pizza.will prefer pepperoni pizza.

1177

3322

ss

320320=

1177

3322

170170

320320=

Your turn !Your turn !

1.1. A survey at school found that 6 out A survey at school found that 6 out of every 10 students have access to of every 10 students have access to the internet at home. If there are the internet at home. If there are 250 students at the school, about 250 students at the school, about how many have internet access at how many have internet access at home?home?

2.2. Luther won 12 of the last 20 video Luther won 12 of the last 20 video games he played. Suppose he plays games he played. Suppose he plays a total of 60 games over the next a total of 60 games over the next month. Predict how many of these month. Predict how many of these games Luther will win.games Luther will win.

Every tenth student entering the school was asked which one of the four subjects was his or her favorite.1. Find the probability that any

student attending school prefers science.

Every tenth student entering the school was asked which one of the four subjects was his or her favorite.2. There are 400 students at the

school. Predict how many students would prefer science.