A survey conducted about smartphone usage habits of residents in certain barangay in Valenzuela. The result of the survey according to age is shown in the following table. Find the mean and the range...

A survey conducted about smartphone usage habits of residents in certain barangay in Valenzuela. The result of the survey according to age is shown in the following table. Find the mean and the range using class boundaries.

56 CHAPTER 4: STATISTICS AND DATA MANAGEMENT LEARNING OBJECTIVES 1. Define Statistics and Describe the range of applications of statistics. 2. Determine and assess the different types of Descriptive Statistics. 3. Define Data and Data Management 4. Construct and Organize data using graphs and charts and evaluate data using the different types of statistical tools. 4.1 STATISTICS ➢ Statistics is the science of collecting, describing, interpreting data and making decisions based on data. • For instance, collecting numerical facts and figures about the number of people tested positive for Corona virus disease 2019 (COVID-19), then describing the possibility of how they got infected, tracing other people who may be exposed to them and may also be infected and in the end would come up with list of recoveries, deaths and those that needs to be quarantined. Statistics showed that a pandemic of respiratory disease is spreading from person to person caused by novel corona virus. • Statistics is so indispensable that bankers used it to estimate the number of clients who will be making deposits as compared to the number of clients requesting for loans, businesses rely on census data to determine the population in a given area, ages, income, educational attainment, occupations, etc. of possible customers. • It is a professional tool to systematically organize data, to reveal and quantify hidden patters from chaos, to summarize or to categorize variations from population, to investigate complicated human behaviors, to make prediction based on existing knowledge, to review and to assess existing technologies and methods and to conceptualize new ideas which may lead to improvements. • Statistics is a branch of applied mathematics its applications can also be found in integration, differentiation, and algebra. 4.2 BRANCHES OF STATISTICS 1. Descriptive Statistics Descriptive statistics is the term given to the analysis of data that helps describe, show, or summarize data in a meaningful and useful way. For example, the GPA of students in a class can be listed from highest to lowest for every subject and the students can be categorized accordingly. The process of descriptive statistics can be carried out using the measures of central tendency and measures of spread. In this process it is useful to summarize group of data using tables, graphs, and statistical analysis. 2. Inferential Statistic Inferential statistics is used to make predictions or comparisons about a larger group (population) using information gathered about a small part of population. It is produced through complex mathematical calculations that scientist used to infer. 57 Inferential statistics is generally used when the user needs to make a conclusion about the whole population at hand, and this is done using the various types of tests such as Linear Regression Analysis, Analysis of Variance, Analysis of Co-variance, Statistical Significance (T- Test) and Correlation Analysis. 4.3 DATA MANAGEMENT Data refers to information coming from observations, counts, measurements, or responses. They are collection of facts and figures and individual pieces of information recorded and used for the purpose of analysis. Data are raw information from which statistics are created. Example 1: Information from the profile of students like age, course, gender, year level, income of parents, etc. Another example are consumers preferences such as their soap, shampoo, toothpaste, lotion, etc. Data management is a process that includes acquiring, validating, storing, protecting, and processing required data to ensure the accessibility, reliability, and timeliness of the data for its users. Example when making business decisions, commercial and industrial companies rely on big data to gain deep insights into customer behavior, trends, and opportunities for creating extraordinary customer experiences. 4.4 DATA COLLECTION Data collection is defined as the procedure of collecting, measuring, and analyzing accurate insights for research using standard validated techniques. The objective of data collection is to ensure that the information collected are of quality and reliable and can be subjected to statistical analysis. 4.5 SOURCES OF DATA I. Primary Data These are raw data which has just been collected from the source and has not gone in any kind of statistical treatment like sorting and tabulation. It may be referred to as firsthand information. The important sources of primary data are primary units such as individuals, households, published sources (data that are available in print or in electronic including those found on internet web sites), basic experimental units. Methods used to collect primary data can be any of the following: 1. Survey – most used to assess thoughts, opinions and feelings. It is often used in social sciences, management, marketing and psychology to some extent. Some ways to conduct a survey are as follows: a. Questionnaire – Interviewing involves asking questions and getting answers from participants in a study. It can be face-to-face interviews and face-to-face group interviewing. Questions may consist of open-ended or close ended questions. It can be conducted via telephone, mail, personal appearance, e-mail or through fax. b. Interview – face to face conversation with the respondent. 2. Experiments – most suitable for medicine, psychological studies, and nutrition. 3. Observations – can be done in natural settings as well as in artificially created environment. II. Secondary Data These are data which has already been collected, sorted, tabulated, and has undergone a statistical treatment and is available in either published or unpublished form. For instance, those data that can be found from the review of literature, from books, biographies, archives. They are called fabricated or tailored data. 58 The following are sources of secondary data: 1. Government Offices and Semi government offices 2. Teaching and research organizations, (NSO, PSA etc) 3. Books, Biographies, Research journals, articles, and newspapers 4. Internet and websites 5. Libraries, data bases, etc. 4.6 TWO BROAD CATEGORIES OF DATA I. QUALITATIVE DATA, (Categorical) Qualitative data are mostly non-numerical and usually descriptive or nominal in nature. They may be observed and described by words, pictures, and symbols but not numbers, because they cannot be expressed in numerical form and therefore cannot be calculated or computed. Often (not always) such data captures feelings, emotions, or subjective perceptions of something. Example 2: Hair color, Gender, ethnic groups, nationality, educational qualification, intelligence, honesty, marital status and other attributes of the population. II. QUANTITATIVE DATA, (Numerical) Quantitative data is numerical in nature and can be mathematically computed. It answers key questions “how many”, “how much” and “how often”. Quantitative data are easily amenable to statistical manipulation and can be represented by a wide variety of statistical types of graphs and charts such as line, bar graph, scatter plot, etc. Example 3: Number of enrollees in your course this school year, height and weight of children, distance travelled from home to office, scores in an examination, prices of commodities, salaries of workers, etc. Table 4.0: Types of data based on their mathematical properties Based on their Mathematical Properties Examples TYPES OF DATA Ordered with their increasing ➢ Accuracy ➢ Powerfulness of measurement ➢ Preciseness ➢ Wide application of statistical techniques NOMINAL Gender (Male, Female) Marital Status (Single, Married, Widowed, Separated) Nationality (Filipino, Chinese, Korean) ORDINAL Rank in competition (First, Second, Third) Rating (Excellent, Good, Fair, Poor) Economic Status (Low, Medium, High) INTERVAL Temperature in degree Celsius Standardized Examination Scores Weighing Scales showing equal intervals RATIO Weight of Toddlers Heights of growing children Age of human Nominal Data Nominal data represents discrete units and are used to label variables that have no quantitative value. It is used for classification purposes. Numbers or letters may be used to represent nominal measurements. Nominal scales are said to be the least powerful in measurement with no arithmetic origin, order, direction, or distance relationship, reason why it has limited or restricted use. 59 Ordinal Data This type of data represents discrete and ordered units. The order of the values is what is important and significant, but the differences between each one is not really known. Ordinal scales are typically the measure of non-numeric concepts like satisfaction, happiness, discomfort, etc., and because they only show sequence, arithmetic cannot be done with it. Interval (Score/Mark Data) These are set of numerical measurements in which the distance between numbers are known, constant size or equal. But they do not have a “true zero”. Interval scales are great, but ratios cannot be calculated. Interval data are more powerful than ordinal scale due to equality of intervals. Ratio Data Ratio data is defined as quantitative data, having the same properties as interval and definitive ratio between each data and absolute “zero” being treated as a point of origin, which means there can be no negative numerical value in ratio data. The most precise data and allow for application of all statistical techniques. Summarizing the types of data: Nominal variables are used to “name” or label a series of values, ordinal data provide good information about order of choices, such as customer satisfaction survey. Interval scales give us the order of values and the ability to quantify the difference between each one. And ratio scales provide the order, interval values plus the ability to calculate ratio since a “true zero” can be defined. DISCRETE DATA AND CONTINUOUS DATA Discrete Data Discrete data has values that are distinct and separate. It represents items that can be counted and only involves integers. It should be converted to continuous data when possible to obtain a high level of information and details.