Introduction to statistics
- 1. Introduction to statistics Mrs.Mayuri Amit Joshi Assistant Professor( Department of Mathematics) Changu Kana Thakur ACS college, New Panvel
- 2. Statistics • The science of collectiong, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions • Statistical analysis – used to manipulate summarize, and investigate data, so that useful decision-making information results.
- 3. Why study statistics? 1. Data are everywhere 2. Statistical techniques are used to make many decisions that affect our lives 3. No matter what your career, you will make professional decisions that involve data. An understanding of statistical methods will help you make these decisions efectively
- 4. Applications of statistical concepts in the business world • Finance – correlation and regression, index numbers, time series analysis • Marketing – hypothesis testing, chi-square tests, nonparametric statistics • Personel – hypothesis testing, chi-square tests, nonparametric tests • Operating management – hypothesis testing, estimation, analysis of variance, time series analysis
- 5. Statistical data The collection of data that are relevant to the problem being studied is commonly the most difficult, expensive, and time-consuming part of the entire research project. Statistical data are usually obtained by counting or measuring items. Primary data are collected specifically for the analysis desired Secondary data have already been compiled and are available for statistical analysis A variable is an item of interest that can take on many different numerical values. A constant has a fixed numerical value.
- 6. Data Statistical data are usually obtained by counting or measuring items. Most data can be put into the following categories: • Qualitative - data are measurements that each fail into one of several categories. (hair color, ethnic groups and other attributes of the population) • quantitative - data are observations that are measured on a numerical scale (distance traveled to college, number of children in a family, etc.)
- 7. Qualitative data Qualitative data are generally described by words or letters. They are not as widely used as quantitative data because many numerical techniques do not apply to the qualitative data. For example, it does not make sense to find an average hair color or blood type. Qualitative data can be separated into two subgroups: dichotomic (if it takes the form of a word with two options (gender - male or female) polynomic (if it takes the form of a word with more than two options (education - primary school, secondary school and university).
- 8. Quantitative data Quantitative data are always numbers and are the result of counting or measuring attributes of a population. Quantitative data can be separated into two subgroups: • discrete (if it is the result of counting (the number of students of a given ethnic group in a class, the number of books on a shelf, ...) • continuous (if it is the result of measuring (distance traveled, weight of luggage, …)
- 9. Types of variables Variables Quantitative Qualitative Dichotomic Polynomic Discrete Continuous Gender, marital status Brand of Pc, hair color Children in family, Strokes on a golf hole Amount of income tax paid, weight of a student
- 10. Numerical scale of measurement: • Nominal – consist of categories in each of which the number of respective observations is recorded. The categories are in no logical order and have no particular relationship. The categories are said to be mutually exclusive since an individual, object, or measurement can be included in only one of them. • Ordinal – contain more information. Consists of distinct categories in which order is implied. Values in one category are larger or smaller than values in other categories (e.g. rating-excelent, good, fair, poor) • Interval – is a set of numerical measurements in which the distance between numbers is of a known, sonstant size. • Ratio – consists of numerical measurements where the distance between numbers is of a known, constant size, in addition, there is a nonarbitrary zero point.