Introduction to Probability and Statistics

Consultation time:

Ms. Chong

OUTLINEOUTLINE

1-1 Introduction1-2 Descriptive and Inferential

Statistics1-3 Variables and Types of Data1-4 Data Collection and Sampling

Techniques1-5 Computers and Calculators

OBJECTIVESOBJECTIVESDemonstrate knowledge of all statistical

terms.

Differentiate between the two branches of statistics.

Identify types of data.

Identify the measurement level for each variable.

Identify the four basic sampling techniques.

Explain the importance of computers and calculators in statistics.

1-1 Introduction1-1 Introduction

What is statistics?

Number ?

Value ?

Data ?

Statistics consists of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data.

Data are the values (measurements or observations) that the variables can assume.

Variables whose values are determined by chance are called random variables.

1-2 Descriptive and Inferential 1-2 Descriptive and Inferential StatisticsStatistics

Descriptive statistics consists of the collection, organization, summarization, and the presentation of data.

Inferential statistics consists of performing estimations and making decision about the whole population based on the information gained from limited samples.

Involve the use of

“statistical terms” for the

data descriptions.

“Describe” the data that

have been collected.

Descriptive Descriptive StatisticsStatistics

Examples of Descriptive Statistics

Six out of ten students in UCSI are local students.

Average score for Biology test is 75.8.

The average annual salary for staffs in Company A is RM 2500.

Draw conclusions and make decisions

Make predictions

Inferential Inferential StatisticsStatistics

Examples of Inferential Statistics

The population in Malaysia will increase by 5% in the coming five years.

It was estimated that the number of cars sold in next month is 50.

Making predictions and estimations

Relief constipati

on problem.

Patients with

constipation

problem.

Eat diet high in fiber.

Examples of Inferential Statistics

Diet high in fiber can help to reduce constipation problem.

Making Conclusion

A population consists of all subjects (human or otherwise) that are being studied.

A sample is a group of subjects selected from a population.

Population

Sample

• Generally, researchers generalize their findings on population based on the sample selected.

• The sample must be representative enough to reflect the whole population.

• The sample is considered representative if:

The sample size was large enough. The sample was selected randomly (no bias).

1-3 Variables and Types of Data1-3 Variables and Types of Data

Data

Qualitative Quantitative

Discrete Continuous

Qualitative VariablesQualitative Variables

Qualitative variables are variables that can be placed into distinct categories, according to the attribute or characteristic.

It also can be known as non-numerical variables.

Example: Gender

Nationality

Marital status

Quantitative VariablesQuantitative Variables

Quantitative variables are numerical and can be ordered or ranked.

It also can be known as numerical variables.

Example: Height

Age

Blood Pressure

Discrete VariablesDiscrete Variables

Discrete variables assume values that can be counted.

Example: Number of student, pairs of shoes, price, etc.

Continuous VariablesContinuous Variables

Continuous variables can assume all values between any two specific values.

They are obtained by measuring instead of counting.

Example: Weight, height, volume, pressure, etc.

Level of MeasurementLevel of Measurement

Classify data according to how they are categorized, counted, or measured.

There are four level of measurement.

Nominal

Interval

Ratio

Ordinal

Norminal level of measurementNorminal level of measurement

Classify data into mutually exclusive categories in

which no order or ranking can be imposed on the data.

Example: Course studied (Medicine/Food Science, etc.)

Eye colour (brown/blue, etc.)

Gender (Male/Female)

Ordinal level of measurementOrdinal level of measurement

Classify data into categories that can be ranked;

however, no precise differences exist between

the ranks.

Example: Grade (A, B, C, D)

Performance (poor, fair, good, excellent)

Judging (first place, second place, etc.)

PerformancePerformance

Poor Fair Good Excellent

Is the difference between poor and fair same as the difference between good excellent?

Are the differences measurable?

Interval level of measurement

Ranks data, and precise differences between the

units of measure do exist.

There is no true / meaningful zero.

Example: IQ (109, 110, etc.)

Temperature (- 5oC, 0oC, 8oC, 10oC, etc.)

Ratio level of measurement

Possesses all characteristics of interval measurement.

A true zero do exists.

Additionally, true ratios exist for the same variable.

Example: Salary (RM0, RM1000, RM3000, etc.)

Weight (0kg, 35kg, 70kg, etc.)

1-4 Data collection and 1-4 Data collection and Sampling Techniques Sampling Techniques

Data can be collected via different methods.

Survey is one of the most commonly used methods.

Surveys can be done through telephone, mail questionnaire, personal interviews, etc.

Sampling MethodsSampling Methods

There are four basic sampling methods are used by statisticians to obtain samples that are unbiased.

Random SamplingRandom Sampling

The samples are selected by chance methods or random numbers.

Systematic SamplingSystematic Sampling

1 2 3 4…10…15…20…25.…30…35

Cluster SamplingCluster Sampling

The population is divided into many clusters.

Samples are selected by using some intact groups that are representative of the population.

POPULATION

A C

D

B

E

A C

E

Samples

Stratified SamplingStratified Sampling

Population is divided into many groups (strata) according to some characteristics.

The subjects within groups are randomly selected as samples for study.

POPULATION

A

C

B

D

A

B

C

D

50 samples

50 samples

50 samples

50 samples

1-5 Computers and Calculators1-5 Computers and Calculators

Computers and calculators make numerical computation easier.

There are many statistical packages available such as Microsoft Excel, MINITAB, SPSS, Unscrambler, etc.

Data must still be understood and interpreted.