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Introduction to Statistics by Ana Sofia Mariano - Coggle Diagram
Introduction to Statistics by Ana Sofia Mariano
Data
What is statistics? Applied mathematics that deals with collection, organization, presentation, analysis, and interpretation of numerical data in order to make desicions.
What is data? Consists of information coming from observations, counts, measurements, or responses.
Data Sets: Population: The collection of all outcomes, responses, measurements, or counts that are of interest. Sample: A subset of the population.
Example: Identifying Data Sets In a recent survey, 4501 adults in the Philippines were asked if they think global warming is a problem that requires immediate government action. Nine hundred thirty-nine of the adults said yes. Identify the population and the sample. Describe the data set.
Solution: Identifying Data Sets • The population consists of the responses of all adults in the PHL. • The sample consists of the responses of the 1526 adults in the PHL in the survey. • The sample is a subset of the responses of all adults in the PHL. • The data set consists of 824 yes’s and 702 no’s.
Parameter and Statistics
Parameter: A number that describes a population characteristic. Average age of all people in the United States
Statistic: A number that describes a sample characteristic. Average age of people from a sample of three states.
Decide whether the numerical value describes a population parameter or a sample statistic. A recent survey of a sample of NBAs reported that the average salary for an NBA is more than Php82,000. Solution: Sample statistic (the average of Php82,000 is based on a subset of the population)
Branches of Statistics
Inferential Statistics: Involves using sample data to draw conclusions about a population.
Descriptive Statistics: Involves organizing, summarizing, and displaying data. e.g. Tables, charts, averages.
Example: A teacher arranges the scores obtained b y his students in a graph - Descriptive A researcher may wish to find out whether exposure to pollution may reduce life span - Inferential
Data Classification
Primary data. They refer to information which is directly gathered from respondents or which is based on direct or firsthand experience. Example: diary.
Secondary data. They refer to information which is taken from published or unpublished data gathered by other individuals or agencies. Example: magazine, books
Example: Classifying Data by Type The base prices of several vehicles are shown in the table. Which data are qualitative data and which are quantitative data?
Solution: Classifying Data by Type
Types of data
Types of variables
Quantitative variables: Numerical measurements or counts.
Qualitative Variable Consists of attributes, labels, or nonnumerical entries.
Methods of collecting data
Interview Method • A. Direct method- the researcher personally interview the respondent. • B. Indirect method- the researcher uses a telephone to interview the respondent.
Questionnaire Method is a list of well-planned questions written on paper, which can be either personally administered or mailed by the researcher to the respondents.
Observation Method the researcher observes the subject of the study which may be an individual, a group, or any unit of interest .4. Registration Method • Examples of data gathered using this method are those obtained from National Statistics Office(NSO), Land Transportation, Department of Education, and other government agencies. .
Mechanical Devices The devices that can be used when gathering data for social and educational researches are the camera, projector, tape recorder, etc. In chemical, biological and medical researches, the common devices are x-ray machine, CT scan, microscope, etc. In astronomy and atmospheric researches, the telescope, barometer, radar machine, computer, etc.
Classification of quantitive variables
Continuous data - numerical responses that arise from a measurement process. Ex. 1.234 in, 2.8 cm 2.
Discrete data -these are numerical responses that arise from a counting process. Ex. Number of children in a community
Levels of measurement
Nominal level of measurement • Qualitative data only • Categorized using names, labels, or qualities •No mathematical computations can be made
Ordinal level of measurement • Qualitative or quantitative data • Data can be arranged in order • Differences between data entries is not meaningful
Example: Classifying Data by Level Two data sets are shown. Which data set consists of data at the nominal level? Which data set consists of data at the ordinal level? Solution: Classifying Data by Level Ordinal level (lists the rank of five TV programs. Data can be ordered. Difference between ranks is not meaningful.)Nominal level (lists the call letters of each network affiliate. Call letters are names of network affiliates.)
Interval level of measurement •Quantitative data •Data can ordered •Differences between data entries is meaningful •Zero represents a position on a scale (not an inherent zero – zero does not imply “none”)
Ratio level of measurement •Similar to interval level •Zero entry is an inherent zero (implies “none”) •A ratio of two data values can be formed •One data value can be expressed as a multiple of another
Sampling Techniques
Random Sampling selects a sample using the concept of the lottery method.
Systematic Sample • Choose a starting value at random. Then choose every kth member of the population. In the West Ridge County example you could assign a different number to each household, randomly choose a starting number, then select every 100th household.
Probability Sampling it is a sampling technique in which every individual in a population has an equal chance of being selected to be a member of the sample.
Stratified Sample selects a sample when the population is segmented into groups or sections called stratifications or strata.To collect a stratified sample of the number of people who live in Angeles City households, you could divide the households into socioeconomic levels and then randomly select households from each level.
Non-Probability Sampling 1. Purposive Sampling select the sample respondents based on certain criteria laid down by the researcher. 2. Quota Sampling samples are selected using quota system. 3. Convenience Sampling the researcher picks his sample respondents from the population that he finds convenient to interview due to their availability or accesability.
Cluster Sample • Divide the population into groups (clusters) and select all of the members in one or more, but not all, of the clusters. In Pampanga example you could divide the households into clusters according to zip codes, then select all the households in one or more, but not all, zip codes.