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• Descriptive Statistics: organization, summary, and description of data.

• Inferential Statistics: reach decisions about a population by examining a sample.

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• Data types:

  • Quantitative data: numbers (e.g., weights, ages).

  • Qualitative data: words (e.g., nationalities, occupations).

• Statistics: descriptive statistics (data collection, organization, summary, analysis) and inferential statistics (inferences about population from a sample).

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• Biostatistics: data from biological sciences and medicine.

• Sources of Data: 1) Routinely kept records, 2) Surveys, 3) Experiments, 4) External sources (published reports, data banks, …).

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• Population: the largest collection of elements of interest at a time, about which we want to draw conclusions.

• When measuring a variable on each population element, we generate a population of values.

• Population Size: $N$ denotes the number of elements in the population.

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• Sample: a part of the population selected for data collection.

• From the population, we collect data on a subset (sample).

• Sample Size: $n$ denotes the number of elements in the sample.

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• Example: study weights of students in the College of Engineering at KSU.

• If we randomly select $n = 50$ students and measure their weights, the weights form the sample.

• Population: All students enrolled in the College of Engineering at KSU.

• Sample: $n = 50$ students.

• Variable: Weight of students.

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• Variable: a characteristic measured on elements; values vary across elements.

• Examples: 1) No. of patients, 2) Height, 3) Sex, 4) Educational Level.

• Types of Variables: Quantitative and Qualitative.

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1) Quantitative Variables: measurable characteristics; values are numbers indicating amount.

• (a) Discrete Variables: jumps between values.

  • Family size $x = 1, 2, 3, \,dots$

  • Number of patients $x = 0, 1, 2, 3, \,dots$

• (b) Continuous Variables: no gaps; any value within an interval.

  • Height $140 < x < 190$

  • Blood sugar level $10 < x < 15$

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2) Qualitative Variables: values are words indicating category.

• (a) Nominal Qualitative Variables: categories are mutually exclusive and non-ranked.

  • Blood type (O, AB, A, B)

  • Nationality (Saudi, Egyptian, British, …)

  • Sex (male, female)

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(b) Ordinal Qualitative Variables: categories are mutually exclusive and ranked.

• Educational level (elementary, intermediate, …)

• Students grade (A, B, C, D, F)

• Military rank

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Variables

• Quantitative Variables: Discrete (Family Size, No. of Patients); Continuous (Age, Height)

• Qualitative Variables: Nominal (Blood type, Sex); Ordinal (Student grade, Military rank)

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• Sampling and Statistical Inference

• Simple Random Sampling: If a sample of size $n$ is selected from a population of size $N$ such that each element in the population has the same chance to be selected, the sample is a simple random sample.

• Stratified Random Sampling: Elements are classified into homogeneous groups (strata). From each group, an independent simple random sample is drawn. The sample resulting from combining these samples is a stratified random sample.