Statistics is the study of collecting, organizing, analyzing, and interpreting numerical data. It has two main branches: descriptive statistics, which describes characteristics of a data set, and inferential statistics, which draws conclusions about a population based on a sample. Key concepts in statistics include populations, samples, parameters, statistics, variables, and data types.
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M A T H30 2 Lecture1b
1. StatisticsThe branch of mathematics that deals with the collection, organization, analysis, and interpretation of numerical data. Statistics is especially useful in drawing general conclusions about a set of data from a sample of the data.A scientific study of knowledge that deals withCollection of dataOrganization/presentation of dataAnalysis and interpretation of data
2. Branches of StatisticsDescriptive Statistics is a statistical procedure concerned with describing the characteristics and properties of a group of persons, places or things. It is based on easily verifiable facts.Descriptive Statistics can answer questions such as:How many students have failed MATH30-2 thrice?What are the highest and lowest scores in the final exam?What insurance policies/products have appealed the public most?What proportion of Filipinos will vote for Noynoy?How many passed in the recent nursing licensure exam?
3. Branches of StatisticsInferential Statistics draws inferences about the population based on the data gathered from the samples using the techniques of descriptive statistics.Remark: DS is the backbone of IS.Inferential Statistics can answer questions like:Is there a significant relation between the amount of election expenses and popularity among voters?Is there a significant correlation between the amount spent in studying and final grade in a Math course?Is there a significant correlation between the height of a player and his total points in a basketball game?Remark: In IS, one tries to arrive at conclusions that extend beyond the immediate data alone.
4. Population and SamplePopulation – a large collection of objects, places, or things.Parameter – any numerical value that describes a population. Example: There are 5,786 students enrolled in MATH10-1. Population: students of MATH10-1 Parameter: 5,786Sample – a small portion or part of a population; a representative of the population in a research study.
5. Population and SampleStatistic – any numerical value that describes a sample. Example: Of the 5,786 students enrolled in MATH10-1, 3,456 are female. Population: students of MATH10-1 Parameter: 5,786 Sample: Female students in MATH10-1 Statistic: 3,456Issues in sample:How to choose the sample?How large the sample should be?Does the sample reflect the entire population?
6. DataData are facts (a set of infomation) gathered or under study.Types of DataPrimary Data – refer to information which are gathered directly from an original source or which the researcher gathered himself.Secondary Data – refer to information which are taken from published or unpublished data previously gathered by other individuals or agencies.Quantitative Data – numerical in nature and therefore, meaningful arithmetic can be done.Qualitative Data – attributes which cannot be subjected to meaningful arithmetic.
7. Examples: Classify as QN/QLWeekly allowanceIncome of parentsGenderCivil StatusReligionAgeAddressEducational attainmentJobsSchools attended
8. Types of Quantitative DataDiscrete data – assume exact values only and can be obtained by counting. Example: Number of studentsContinuous data – assume infinite values within a specified interval and can be obtained by measurement. Example: Height
9. State whether discrete or continuous.The number of hair-transplant sessions undergone in the past year.The time since the last patient was grateful for what you did.The amount of weight you’ve put on in the last year.The number of hairs you’ve lost in the same time.
10. VariableA variable is simply what is being observed or measured.A property of a population/sample which makes the members different Example: Gender of students in MapuaDependent variable – the outcome of interest, which should change in response to some intervention.Independent variable – the intervention, or what is being manipulated.Example: Number of hours spent in studying and test scores
11. ConstantA property of a population/sample which makes the members similar Example: Gender in a class of all boys
12. Variables According to Scale of MeasurementNominal Variable - has no meaning (e. g. SSS No.) - consists of named categories, with no implied order among the categoriesOrdinal Variable - used to label rank - consists of ordered categories, where the differences between categories cannot be considered to be equal Example: A student evaluation rating consisting of Excellent/Satisfactory/Unsatisfactory has three categories.
13. Variables According to Scale of MeasurementInterval Variable - has no true zero. - has equal distances between values, but the zero point is arbitrary. Examples: Temperature IQ (difference between 70 and 80 is same as 120 and 130; an IQ of 100 does not mean twice the IQ of 50)Ratio Variable - has true zero. - has equal intervals between and a meaningful zero point. Examples: Physical characteristics (height and weight)