Unit 9 Probability & Statistics

Types of Probability Section 9.1

- Theoretical probability

- Experimental Probability

- Subjective Probability (judgement)

Theoretical probabilityThe probability or likelihood that an event will happen.

P(event) = Number of favourable outcomes / Total number of possible outcomes

Ex 2: If we toss a coin what is the probability that tails will show up?

Ex 2: A bag contains 20 marbles. 15 of them are red and 5 of them are blue in colour. What is the probability of picking a red marble?

Experimental probabilityThe ratio of the number of times an event occur to the total number of trials.

Ex 1: Sam rolled a number cube 50 times. A 3 appeared 10 times. What is the experimental probability of rolling a 3?

The probability of rolling a 3 is 10 out of 50 or 20%

Subjective probability (judgement)

Derived from an individual's personal judgement about whether a specific outcome is likely to occur.

Subjective probabilities contain no formal calculations and only reflect the persons opinions or past experience.

Factors that lead to problems with data collection

Section 9.2

Bias Cultural Sensitivity

Use of language Ethics

Timing Cost

Privacy Time

See page 432 for

examples!

Factors that lead to problems with data collection

Bias: the question influences responses in favour of, or against the topic of the data collection.

Use of language: the use of language in a question could lead people to give a particular answer.

Timing: When the data are collected could lead to particular results.

Privacy: if the topic of the data collection is personal, a person may not want to participate or may give untrue answers on purpose.

Cultural sensitivity: means that you are aware of other cultures. You must avoid being offensive and asking questions that do not apply to that culture.

Ethics: ethics dictate that collected data must not be used for purposes other that those told to the participants. Otherwise actions could be unethical.

Cost: the cost of collecting data must be taken into account.

Time: the time needed for collecting the data must be considered.

Sample, Population, & Census (Section 9.3)

Population: when collecting data, the group about which you are getting information.

Sample: a small portion chosen which is representative of a population.

Census: a data collection from the entire population.

Selecting a sample Section 9.4

Simple random sample

Systematic or interval sampling

Cluster sampling

Self-selected sampling

Convenience sampling

Stratified random sample

Simple random sample Each member of the population has an equal chance of being selected

Example: to select a random sample from your math class, each student is assigned a number and 5 numbers are drawn from a hat.

Systematic or interval sampling

Every n'th member of the population is selected.

Example: every 20th product in an assemble line is tested for quality control.

Cluster samplingEvery member of each randomly chosen group of the population is selected.

Example: each grade represents a group in a school population. One grade in your school is chosen randomly, and all students in that grade are selected.

Self-selected sampling

Only members who are interested and volunteer will participate.

Example: if a radio station conducts a telephone survey, only people who are interested will call in.

Convenience sampling

Only members of the population who are convenient to include are selected.

Example: for a survey about grocery shopping habits, people in a grocery store are approached and questioned.

Stratified random sampling

Some members from each group of the population are randomly selected.

Example: 5 randomly chosen students from each grade in a school could be selected, even if each grade has a different number of students.