Descriptive Statistics Review PDF

DESCRIPTIVE STATISTICS A Review Statistics- is the science that deals with the collection of data, organization, interpretation, analysis and data presentation. Branches of Statistics Basic Concepts 1. Variable- a characteristic that can be measured and that can assume different values. Examples:...

DESCRIPTIVE STATISTICS A Review Statistics- is the science that deals with the collection of data, organization, interpretation, analysis and data presentation. Branches of Statistics Basic Concepts 1. Variable- a characteristic that can be measured and that can assume different values. Examples: Height, age, income, province or country of birth, grades obtained at school and type of housing 2. Data- a specific measurement of a variable 2.1 Qualitative/Categorical Data- names or labels that divide the data into specific categories Examples: birth location, gender, religion affiliation 2.2 Quantitative Data- numerical values that can either be counted or measured Examples: grades, height, age, class size 2.2.1 Discrete- numerical values that can be counted Examples: number of employees, no. of books in the library, population in a barangay 2.2.2 Continuous- numerical values that can be measured Examples: height, weight, temperature Basic Concepts 4. Sources of Data 4. 1 Primary data- data collected from the original source, using methods like interviews, diaries, surveys and censuses 4.2 Secondary data- secondhand information and commentary made by other researchers like newspaper, encyclopedias, academic books, journal articles 5. Parameter- is a characteristic /number describing a whole population 6. Statistic – is a characteristic / number describing a sample 7. Population-encompasses all the individuals, items, or observations under study 8. Sample- subset of the population carefully selected to represent its characteristics Basic Concepts 9. Levels of Measurement 9.1 Nominal - categorizes variables according to qualitative labels (or names). Examples: hair color, gender/sex 9.2 Ordinal - categorizes variables into labeled groups, and these categories have an order or hierarchy to them. Examples: Level of Education- Elementary, High school, master’s degree, Doctorate degree 9.3 Interval - is a numerical scale which labels and orders variables, with a known, evenly spaced interval between each of the values.is a characteristic /number describing a whole population Examples: IQ score, temperature 9.4 Ratio – The ratio scale is exactly the same as the interval scale, with one key difference: The ratio scale has what’s known as a “true zero.” Examples: Weight, Height, age Basic Concepts 10. Sampling Techniques 10.1 Probability Sampling 10.1.1 Simple Random – is a technique in which each member of a population has an equal chance of being chosen through unbiased selection method like the lottery method and the “fish bowl” method. 10.1.2 Systematic Random - the random sampling method that requires selecting samples based on a system of intervals in a numbered population 10.1.3 Stratified Random Sampling - the random sampling method that requires selecting samples based on a system of intervals in a numbered population 10.2 Non-Probability Sampling 10.2.1 Purposive Sampling –intentionally selecting participants based on their characteristics, knowledge, experiences, or some other criteria. 10.2.2 Cluster/ Area Sampling – probability sampling technique where researchers divide the population into multiple groups (clusters) for research. 10.2.3 Convenience – involves recruiting individuals primarily because they are available, willing, or easy to access or contact on a practical level. Basic Concepts 11. Collection of Data 11.1 Indirect/ Questionnaire - a list of questions or items used to gather data from respondents about their attitudes, experiences, or opinions. It is the most appropriate way of eliciting information from a group of people belonging to diversified classes 11.2 Direct/Interview - used to collect primary data by asking one or more people about their opinions, experiences or perspectives on a particular topic or subject matter 11.3 Experiment - data collection method is used to determine cause and effect relationship 11.4 Registration – data collection enforced by certain laws 12. Presentation of Data 12.1 Time Series – presents data that occur over a specific period; to look for pattern or trend that occurs over the period of time 12.2 Bar Graph – presents the data by using horizontal or vertical bars whose heights or lengths are determined by the frequencies of the data Basic Concepts 12.3 Pie graph -used in showing relationship of the parts to the whole by visually comparing the sizes of the sections 12. 4 Scatter Plot - is a graph of ordered pairs of data values that is used to describe the relationship that exists between two variables 12.5 Frequency Distribution - is the organization of data in tabular form using classes and frequencies Basic Concepts 13. Descriptive Measures 13.1 Measures of Central Tendency 13. 1 Mean – arithmetic average/ the most reliable measure of central tendency 52 + 61 + 53 + 60 + 55 + 47 + 60 + 44 432 𝑥ҧ = 𝑥ҧ = = 54 8 8 13. 2 Median - the number in the middle of a data set 𝑎𝑟𝑟𝑎𝑛𝑔𝑒 𝑡ℎ𝑒 𝑑𝑎𝑡𝑎: 47, 52, 53, 55 60, 60, 61 23 + 25 SET A: 20, 18, 26, 29, 23, 25, 30, 20 𝑎𝑟𝑟𝑎𝑛𝑔𝑒 𝑡ℎ𝑒 𝑑𝑎𝑡𝑎: 18, 20, 20, 23,25, 26, 29, 30 𝑥෤ = = 24 2 13.3 Mode – the most common number that appears in your set of data 𝑥 ̂ = 60 SET A: 23,23,45,67,45,67,23,67 SET B: 23,23,45,67,45,67 Mode: 23 and 67 No mode Basic Concepts 13. Descriptive Measures 13.2 Measures of Variation - indicates the extent to which individual items in a series are scattered about a central value 13.2.1 Range -is obtained by computing the difference of the highest value and the lowest value in a data set 13.2.2 Variance -is obtained by getting the average of the squares of the distance each value is from the mean 13.2.3 Standard Deviation –is obtained by the square root of variance