AAUACSC 111

AAUACSCI 111 Introduction to Statistics for Computer Science

1. Introduction to Computer Science & Statistics

1.1 Meaning of Computer Science

• Computer Science is the study of:

  • Computation

  • Algorithms

  • Data

  • Computer systems

• Focuses on how data is:

  • Collected

  • Processed

  • Stored

  • Transformed into useful information using computers

1.2 Meaning of Statistics

• Statistics is the science of:

  • Collecting

  • Organising

  • Analyzing

  • Interpreting

  • Presenting data

• Purpose: To support decision-making

1.3 Relationship Between Computer Science and Statistics

• Computer Science and Statistics are closely related because:

  • Computer systems generate large volumes of data

  • Statistics provides tools to analyze and interpret this data

  • Many modern CS fields rely heavily on statistical concepts, including:

  • Artificial Intelligence (AI)

  • Machine Learning (ML)

  • Data Science

  • Software Engineering

• Examples of relationships:

  • Performance evaluation of algorithms

  • Software reliability and defect prediction

  • Data mining and machine learning models

1.4 Importance of Statistics in Computing

• Supports decision making under uncertainty

• Aids in analyzing experimental and observational data

• Enables prediction and trend analysis

• Improves system optimization and quality control

1.5 Applications of Statistics in Computer Science

• Artificial Intelligence and Machine Learning

• Data Science and Big Data Analytics

• Software Engineering (testing, reliability analysis)

• Network traffic analysis

• Cybersecurity and fraud detection

2. Fundamentals of Statistics

2.1 Concept of Statistics

• Statistics can be viewed in two ways:

  • As numerical data: Facts and figures obtained through observation

  • As a discipline: A body of methods used to collect, analyze, and interpret data

2.2 Definitions of Statistics

• Statistics is defined as:

2.3 Types of Statistics

• Statistics is broadly divided into two main types: (a) Descriptive Statistics

  • Deals with methods used to summarize and describe data.

  • Examples include:

  • Tables

  • Charts and graphs

  • Measures of central tendency (mean, median, mode)

  • Measures of dispersion (range, variance, standard deviation)
    (b) Inferential Statistics

  • Involves making conclusions or predictions about a population based on sample data.

  • Examples include:

  • Estimation

  • Hypothesis testing

  • Regression and correlation

3. Statistical Data

3.1 Concept of Data

• Data refers to raw facts, figures, observations, or measurements collected for analysis

3.2 Categories of Data

• Data can be categorized into two types: (a) Qualitative Data

  • Non-numerical data

  • Describes attributes or characteristics.

  • Examples:

  • Gender

  • Color

  • Software type
    (b) Quantitative Data

  • Numerical data

  • Can be measured or counted.

  • Examples:

  • Age

  • Number of users

  • Execution time

3.3 Types of Data

(a) Discrete Data

• Countable values

• Examples:

  • Number of students

  • Number of errors
    (b) Continuous Data

• Measurable values within a range

• Examples:

  • Time

  • Temperature

  • Memory usage

4. Data Collection

4.1 Meaning of Data Collection

• Data collection is the process of gathering information for analysis and decision-making.

4.2 Sources of Statistical Data

(a) Primary Data

• Collected firsthand by the researcher.

• Examples:

  • Surveys

  • Interviews

  • Experiments

  • Observations
    (b) Secondary Data

• Collected by others and reused.

• Examples:

  • Journals

  • Government reports

  • Databases

  • Online repositories

4.3 Methods of Statistical Data Collection

• Questionnaires

• Interviews

• Direct observation

• Experiments

• Automated data logging (sensors, software logs)

5. Presentation of Data

5.1 Meaning of Data Presentation

• Data presentation is the process of organizing data in a meaningful way so that it can be easily understood and interpreted.

5.2 Techniques of Data Presentation

(a) Tabular Presentation

• Data is arranged in rows and columns

• Simple and easy to understand
  (b) Graphical Presentation

• Bar charts

• Pie charts

• Histograms

• Line graphs
  (c) Diagrammatic Presentation

• Pictograms

• Flow diagrams

5.3 Importance of Data Presentation

• Makes data easy to understand

• Highlights trends and patterns

• Aids comparison

• Supports effective decision making

6. Measures of Central Tendency

6.1 Meaning of Central Tendency

• Measures of central tendency are statistical values that represent the center or typical value of a dataset.

• They help summarize large datasets with a single representative figure.

6.2 Types of Measures of Central Tendency

(a) Mean

• The mean is the arithmetic average of a set of values.

• Formula: $Mean = \frac{\text{Sum of all observations}}{\text{Number of observations}}$

• Applications in Computer Science:

  • Average execution time of algorithms

  • Average response time of systems

• Advantages:

  • Easy to compute

  • Uses all observations

• Disadvantages:

  • Affected by extreme values (outliers)

  (b) Median

• The median is the middle value when data is arranged in ascending or descending order.

• Applications:

  • Used when data contains extreme values

  • System performance analysis with skewed data

  (c) Mode

• The mode is the value that occurs most frequently in a dataset.

• Applications:

  • Most frequent error type

  • Most common user choice in applications

7. Measures of Dispersion

7.1 Meaning of Dispersion

• Measures of dispersion show how spread out or scattered data values are around the central value.

7.2 Types of Measures of Dispersion

(a) Range

• $Range = \text{Maximum value} - \text{Minimum value}$

• Simple but does not consider all data values.
  (b) Variance

• Variance measures the average squared deviation from the mean.

• Applications:

  • Performance stability analysis

  • System reliability assessment
    (c) Standard Deviation

• Standard deviation is the square root of variance.

• Advantages:

  • Uses all data values

  • Widely used in computing and data science

8. Probability and Its Applications

8.1 Meaning of Probability

• Probability is the measure of the likelihood that an event will occur.

• Probability values range from 0 to 1.

8.2 Basic Probability Concepts

• Experiment: An activity with observable outcomes

• Sample Space: Set of all possible outcomes

• Event: A subset of the sample space

8.3 Applications of Probability in Computer Science

• Machine learning models

• Fault prediction in software systems

• Network reliability analysis

• Cybersecurity risk assessment

9. Introduction to Statistical Inference

9.1 Meaning of Statistical Inference

• Statistical inference involves concluding about a population based on sample data.

9.2 Population and Sample

• Population: Entire set of interest

• Sample: Subset of the population

9.3 Sampling Techniques

(a) Random Sampling

• Every element has an equal chance of selection.
  (b) Systematic Sampling

• Selection at regular intervals.
  (c) Stratified Sampling

• Population divided into groups (strata).

9.4 Importance of Statistical Inference

• Reduces cost and time

• Enables generalization

• Supports decision making in computing research.