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# M A T H30 2 Lecture1b

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### M A T H30 2 Lecture1b

1. 1. Statistics<br />The 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.<br />A scientific study of knowledge that deals with<br />Collection of data<br />Organization/presentation of data<br />Analysis and interpretation of data<br />
2. 2. Branches of Statistics<br />Descriptive 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.<br />Descriptive Statistics can answer questions such as:<br />How many students have failed MATH30-2 thrice?<br />What are the highest and lowest scores in the final exam?<br />What insurance policies/products have appealed the public most?<br />What proportion of Filipinos will vote for Noynoy?<br />How many passed in the recent nursing licensure exam?<br />
3. 3. Branches of Statistics<br />Inferential Statistics draws inferences about the population based on the data gathered from the samples using the techniques of descriptive statistics.<br />Remark: DS is the backbone of IS.<br />Inferential Statistics can answer questions like:<br />Is there a significant relation between the amount of election expenses and popularity among voters?<br />Is there a significant correlation between the amount spent in studying and final grade in a Math course?<br />Is there a significant correlation between the height of a player and his total points in a basketball game?<br />Remark: In IS, one tries to arrive at conclusions that extend beyond the immediate data alone.<br />
4. 4. Population and Sample<br />Population – a large collection of objects, places, or things.<br />Parameter – any numerical value that describes a population.<br /> Example:<br /> There are 5,786 students enrolled in MATH10-1.<br /> Population: students of MATH10-1<br /> Parameter: 5,786<br />Sample – a small portion or part of a population; a representative of the population in a research study.<br />
5. 5. Population and Sample<br />Statistic – any numerical value that describes a sample.<br /> Example:<br /> Of the 5,786 students enrolled in MATH10-1, 3,456 are female.<br /> Population: students of MATH10-1<br /> Parameter: 5,786<br /> Sample: Female students in MATH10-1<br /> Statistic: 3,456<br />Issues in sample:<br />How to choose the sample?<br />How large the sample should be?<br />Does the sample reflect the entire population?<br />
6. 6. Data<br />Data are facts (a set of infomation) gathered or under study.<br />Types of Data<br />Primary Data – refer to information which are gathered directly from an original source or which the researcher gathered himself.<br />Secondary Data – refer to information which are taken from published or unpublished data previously gathered by other individuals or agencies.<br />Quantitative Data – numerical in nature and therefore, meaningful arithmetic can be done.<br />Qualitative Data – attributes which cannot be subjected to meaningful arithmetic.<br />
7. 7. Examples: Classify as QN/QL<br />Weekly allowance<br />Income of parents<br />Gender<br />Civil Status<br />Religion<br />Age<br />Address<br />Educational attainment<br />Jobs<br />Schools attended<br />
8. 8. Types of Quantitative Data<br />Discrete data – assume exact values only and can be obtained by counting.<br /> Example: Number of students<br />Continuous data – assume infinite values within a specified interval and can be obtained by measurement.<br /> Example: Height<br />
9. 9. State whether discrete or continuous.<br />The number of hair-transplant sessions undergone in the past year.<br />The time since the last patient was grateful for what you did.<br />The amount of weight you’ve put on in the last year.<br />The number of hairs you’ve lost in the same time.<br />
10. 10. Variable<br />A variable is simply what is being observed or measured.<br />A property of a population/sample which makes the members different<br /> Example: Gender of students in Mapua<br />Dependent variable – the outcome of interest, which should change in response to some intervention.<br />Independent variable – the intervention, or what is being manipulated.<br />Example: Number of hours spent in studying and test scores<br />
11. 11. Constant<br />A property of a population/sample which makes the members similar<br /> Example: Gender in a class of all boys<br />
12. 12. Variables According to Scale of Measurement<br />Nominal Variable<br /> - has no meaning (e. g. SSS No.)<br /> - consists of named categories, with no implied order among the categories<br />Ordinal Variable<br /> - used to label rank<br /> - consists of ordered categories, where the differences between categories cannot be considered to be equal<br /> Example: A student evaluation rating consisting of Excellent/Satisfactory/Unsatisfactory has three categories.<br />
13. 13. Variables According to Scale of Measurement<br />Interval Variable<br /> - has no true zero.<br /> - has equal distances between values, but the zero point is arbitrary.<br /> Examples:<br /> Temperature<br /> IQ (difference between 70 and 80 is same as 120 and 130; an IQ of 100 does not mean twice the IQ of 50)<br />Ratio Variable<br /> - has true zero.<br /> - has equal intervals between and a meaningful zero point.<br /> Examples:<br /> Physical characteristics (height and weight)<br />