Data Collection, Sampling Techniques, FDT, and Presenting Data PDF

S TAT I S T I C S 3 RD Q UA RT E R BASIC CONCEPTS ON STATISTICS ETYMOLOGY OF STATISTICS - comes from the Latin word “statisticus” meaning “of the state” - derived from the Italian word “statisticum collegium” meaning “council of state” - The German word “statistik” first introduced...

S TAT I S T I C S 3 RD Q UA RT E R BASIC CONCEPTS ON STATISTICS ETYMOLOGY OF STATISTICS - comes from the Latin word “statisticus” meaning “of the state” - derived from the Italian word “statisticum collegium” meaning “council of state” - The German word “statistik” first introduced by Gottfried Achenwall to signify science of state. STATISTICS - is the a scientific body of knowledge that deals with the collection, organization or presentation, analysis and interpretation of data to obtain meaningful information  D ATA COLLECTION 3 RD Q UA RT E R Collection Organization Analysis Interpretation 1. Collection - refers to the gathering of information or data. 2. Organization or Presentation – involves summarizing data or information in textual, graphical, or tabular form. 3. Analysis – involves analyzing the data by using statistical methods and procedures 4. Interpretation – refers to the process of making conclusions based on the analyzed data. DATA SOURCES Population - refers to the totality of objects under consideration. -refers to a large collection of objects, persons, places, things or events which vary with respect to some characteristics. -usually denoted by N. DATA SOURCES Sample is a subset of a population gathered through sampling. The sampling usually done randomly. - usually denoted by n. POPULATION Parameter is any numerical or nominal characteristics of population. It is a value or measurement obtained from a population. SAMPLE statistic is an estimate of a parameter. It is any value or measurement obtained from a sample. TYPES OF DATA Data (singular form datum) are facts or a set of information or observations under study. Data re gathered by the researcher from a population or a sample. TYPES OF DATA Qualitative Data refers to data that are arranged into separate categories. This is also known as categorical data. –Nominal Data (e.g. gender, color, etc) –Ordinal Data (e.g. good, better, best; freshmen, sophomores, juniors, seniors) TYPES OF DATA Quantitative Data – numbers are used to describe data. This can either be discrete or continuous. –Discrete – these are data that cannot be measured but can be counted. (e.g. age, no. of siblings, etc) TYPES OF DATA –Continuous – data that can’t be counted but can be measured. (e.g. height, temperature, weight). These data can be interval or ratio. TYPES OF DATA Interval Data – order of values exist and the difference between two values is meaningful. With interval data, we can subtract and add but we cannot multiply, divide or calculate ratios. With this, there is no true zero in interval scale. (e.g. temperature) TYPES OF DATA Ratio – these are data with all the properties of the interval data except that it has a true zero value. This means that, when a variable equals to 0, there is none of that variable. (e.g. height, weight, etc) USES OF STATISTICS Education – statistics can be used to assess students’ performance and correlate factors affecting teaching and learning processes to improve equality education USES OF STATISTICS Psychology – it is used to determine attitudinal patterns, the causes and effects of misbehavior. Business and economics – statistics is used to analyze a wide range of data like sales, outputs, price indices, revenues, cost and the like. USES OF STATISTICS Research and experimentation – statistics is used to validate or test a claim or inferences about a group of people or object, or series of events. Medicine– statistics is used to collect information about patients and diseases and to make decisions about the use of new treatments. EXAMPLES OF RESEARCHES Research and experimentation – statistics is used to validate or test a claim or inferences about a group of people or object, or series of events. Medicine– statistics is used to collect information about patients and diseases and to make decisions about the use of new treatments. DATA CAN BE COLLECTED THROUGH THE FOLLOWING: Interview Survey/Questionnaire Historical Records Observations Discussions Experiments/Case Studies  METHODS ON DATA COLLECTION 1. Interview or the Direct Method In this method the researcher has direct contact with the interviewee which must be a member of the population. The researcher obtains information needed by asking questions and inquiries from the interviewee. This method is usually used in business research.  METHODS ON DATA COLLECTION 1. Interview or the Direct Method EXAMPLE: A study on the favorite brand of cellphone of Grade 7 students in Makati Science High School  METHODS ON DATA COLLECTION 2. Questionnaire or the Indirect Method This is an alternative method for interview. Responses are obtained by distributing questionnaires, which is a list of question intended to elicit answers to a given problem and must be given in a logical order and not too personal, to the respondents. The researcher distributes the questionnaire via hand- carry, mail, online or by google form. METHODS ON DATA COLLECTION 2. Questionnaire or the Indirect Method EXAMPLE: An evaluation of an online webinar-workshop of Senior High School teachers in National Capital Region METHODS ON DATA COLLECTION 3. The Registration Method This method of collecting data is governed by laws. This is the most reliable data since it is governed by law. METHODS ON DATA COLLECTION 3. The Registration Method EXAMPLE: Research on the unemployment rate in the Philippines over the past decade METHODS ON DATA COLLECTION 4. The Experimental Method This method is usually used to find out cause and effect relationships Scientific researchers often use this method. METHODS ON DATA COLLECTION 4. The Experimental Method EXAMPLE: A study on the effect of vitamin C tablet on the immune system of human ages 60 and above.  SAMPLING TECHNIQUES 3 RD Q UA RT E R SAMPLING METHODS/TECHNIQUES Sampling technique is a procedure used to determine the individuals or members of a sample. There are two types of sampling probability sampling and non- probability sampling. PROBABILITY SAMPLING 1. Probability sampling is a sampling technique wherein each member or element of the population has an equal chance of being selected as members of the sample. There are several probability sampling techniques. PROBABILITY SAMPLING a. Random Sampling is a sampling where subjects are selected using chance methods or random numbers. Each individual in the population has equal chance of being drawn into the sample. PROBABILITY SAMPLING There are two ways of selecting members of this sample, that is through lottery method and table of random numbers. PROBABILITY SAMPLING Lottery method is a method that assign numbers to the subjects, then placed number cards in a bowl, mix them thoroughly and select as many cards as needed. The subject whose numbers are selected constitute the sample. PROBABILITY SAMPLING Table of Random Numbers is a method of obtaining sample by generating random numbers using a computer or calculator. Before the invention of computers, random numbers were obtained by table of random numbers, then select a starting number by closing the eyes and placing your fingers on a number in the table. Then use that as a pattern in finding the other numbers which will form the sample. PROBABILITY SAMPLING b. Systematic Sampling is a sampling where 𝒕𝒉 the subjects are selected by using 𝒌 number after the first subject is randomly selected from 1 through 𝑁. We have to select a random starting point, then consider successive elements from the population, where we 𝒕𝒉 consider every 𝒌.  PROBABILITY SAMPLING Consider starting with C on the population from the example below and consider every 3rd term thereafter. The result will make up your sample.  PROBABILITY SAMPLING Example: Mrs. Vargas wants to select 5 students from her class of 40 students. Solution: First, select a random starting point by dividing the number of people in the population by the number of people in the sample. Divide the number of people in the population by the number of people in the sample.  PROBABILITY SAMPLING We will consider numbers 1- 8 as any starting point. Write numbers 1 to 8 in a paper, put the papers in a container, draw one number by lottery which will be the starting point. If, for instance, we acquired 6, then we will start with the sixth term. Then we will consider every 6th member of the population. Which means we will consider the 6th, 12th, 18th, 24th, and 30th student, based on their class number.  PROBABILITY SAMPLING c. Stratified Random Sampling is a sampling procedure wherein the population is grouped into strata. The word strata (singular stratum), means groups or categories. When we use this strategy, we are actually dividing the elements of a population into different categories and then members of the sample are drawn or selected proportionally from each subgroup. PROBABILITY SAMPLING  PROBABILITY SAMPLING Example: Supposed we have 1,500 residents in the population using 5% margin of error, what is the sample size? How will the sample be allocated in the different barangays below so that the selection will be in proportion to each barangay’s population? East West Barangay Cembo Rembo Pembo Palar Rembo TOTAL N 250 180 320 600 150 1,500 PROBABILITY SAMPLING Solution: Get the sample using Slovin’s Formula. 𝑁 = 1,500 , 𝑒 = 5% = 0.05 𝑁 1,500 𝑛= = = 𝟑𝟏𝟓. 𝟕𝟗 or 𝟑𝟏𝟔 1+𝑁𝑒 2 1+1,500(0.05)2 Find the ratio (𝑘) of 𝑛 to 𝑁. 𝑛 316 𝑘= = = 𝟎. 𝟐𝟏 𝑁 1,500  PROBABILITY SAMPLING Find the allocation per barangay by multiplying the ratio (𝑘) to the population of each barangay. Barangay Cembo East Rembo Pembo Palar West Rembo TOTAL 𝑵 250 180 320 600 150 1,500 Product of 𝒌 & 250 × 0.21 180 × 0.21 320 × 0.21 600 × 0.21 150 × 0.21 population in each = 52.5 = 37.8 = 67.2 = 126 = 31.5 barangay 𝒏 53 38 67 126 32 316 Thus the following are the allocation for the sample in each barangay.  PROBABILITY SAMPLING Another way of doing this is by getting the ratio of every barangay, then multiply the ratio with the sample size as shown below. Barangay Cembo East Pembo Palar West TOTAL Rembo Rembo 𝑵 250 180 320 600 150 1,500 Ratio 250 1 180 3 320 16 600 2 150 1 = = = = = 1,500 6 1,500 25 1,500 75 1,500 5 1,500 10 Product of total 1 3 16 2 1 316 × 316 × 316 × 316 × 316 × sample & each 6 25 75 5 10 ratio = 52.67 = 37.92 = 67.41 = 126.4 = 31.6 𝒏 53 38 67 126 32 316 PROBABILITY SAMPLING d. Cluster Sampling is a sampling wherein groups or clusters instead of individual are randomly chosen and then we select a sample of elements from each cluster or group randomly. It is sometimes called area sampling, because it is applied on geographical basis when the population is large. PROBABILITY SAMPLING Example: Supposed we want to determine the average income of a family in Makati. Let us assume that there are 60 barangays in Makati. We can draw a random sample of 15 barangays using simple random sampling and then certain number of families from each of the 15 barangays can be chosen. PROBABILITY SAMPLING PROBABILITY SAMPLING e. Multi-Stage Sampling is a combination of several sampling techniques. Usually this is used by researchers who are interested in studying a very large population. PROBABILITY SAMPLING Example: This is done by starting the selection of the members of the sample using cluster sampling and then dividing each cluster or group into strata. Then, from each stratum individuals are drawn randomly using simple random sampling. PROBABILITY SAMPLING  NON-PROBABILITY SAMPLING Non-probability sampling is a sampling technique wherein members of the sample are drawn from the population based on the judgement of the researcher. The results of a study that will use this sampling technique are relatively biased. The technique lacks objectivity; thus it is also referred to as subjective sampling.  NON-PROBABILITY SAMPLING a.Convenience Sampling is a used because of the convenience it offers the researcher. Example: If a researcher wishes to investigate the most popular prime-time tv-series by interviewing respondents via landline telephone call. The result of this interview will be biased because the opinions of those without telephone will not be included. NON-PROBABILITY SAMPLING b. Quota Sampling is similar to stratified random sampling, where the proportions of the various subgroups in the population, the only difference is that the selection of the member of the sample is not done randomly.  NON-PROBABILITY SAMPLING c. Purposive Sampling is a sampling based on certain criteria laid down by the researcher and people who satisfies the said criteria are interviewed. The respondents are chosen based on their knowledge of the desired information. NON-PROBABILITY SAMPLING Example: If a researcher wishes to investigate about the history of certain locality, then only people of the locality are considered, which are not representative of the whole population. There might also be people who knows about the history of the locality who are not anymore part of its population at that moment. FREQUENCY DISTRIBUTION TA B L E 3 RD Q UA RT E R FREQUENCY DISTRIBUTION TABLE It is a collection of observations produced by sorting them into classes and showing their frequency or number of occurrences in each class. There are basic types of FDT: Ungrouped and Grouped Data FREQUENCY DISTRIBUTION TABLE: UNGROUPED DATA Suppose we conduct a survey asking 15 households how many pets they have in their home. The results are as follows: 1, 8, 1, 7, 1, 6, 1, 5, 2, 5, 2, 4, 2, 3, 3 FREQUENCY DISTRIBUTION TABLE: GROUPED DATA Lower and Upper Class Limits Lower and Upper Class Boundaries Class Mark (midpoint of the classes) Class Width (size) Cumulative Frequency FREQUENCY DISTRIBUTION TABLE: GROUPED DATA The following are the scores obtained by 40 students of Grade 7 – Masipag in a 100 item- Mathematics quiz. 58 56 45 63 64 70 62 66 40 61 66 47 76 61 75 53 55 84 52 46 54 82 57 42 64 48 41 60 92 65 49 50 75 65 65 44 98 76 51 59 FREQUENCY DISTRIBUTION TABLE: GROUPED DATA STEP 1: Arrange the scores from lowest to highest. STEP 2: Determine the Range. 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 64 65 65 65 66 66 70 75 75 76 76 82 84 92 98 FREQUENCY DISTRIBUTION TABLE: GROUPED DATA STEP 3: Compute the number of Classes (K) K=7 STEP 4: Find the class width. (R/K) 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 64 65 65 65 66 66 70 75 75 76 76 82 84 92 98 FREQUENCY DISTRIBUTION TABLE: GROUPED DATA STEP 5: Lower and Upper Class Limits STEP 6: Lower and Upper Class Boundaries STEP 7: Tally and Frequency 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 64 65 65 65 66 66 70 75 75 76 76 82 84 92 98 FREQUENCY DISTRIBUTION TABLE: GROUPED DATA STEP 8: Determine the class mark. STEP 9: Cumulative Frequency 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 64 65 65 65 66 66 70 75 75 76 76 82 84 92 98  D ATA P R E S E N TAT I O N 3 RD Q UA RT E R METHODS OF PRESENTING DATA Textual Method Tabular Method Graphical Method TEXTUAL METHOD Ungrouped data can be presented in textual form by enumerating characteristics, giving emphasis on significant figures and identifying relevant features of the data. STEM-AND-LEAF PLOT Stem-and-leaf plot is a table which sorts data according to certain pattern. It involves separating a number into two parts. In a two-digit number, the stem consists of the first digit and the leaf consists of the second digit. While in a 3-digit number the stem consists of the first two digits, and the leaf consists of the last digit. In one-digit number the stem is zero. STEM-AND-LEAF PLOT STEM LEAF 0 3, 9 1 0, 0, 3, 3, 4, 5, 7, 8, 8, 9 2 0, 0, 0, 1, 5, 6, 6, 7, 8, 8, 8, 8, 9 3 0, 0, 1, 2, 2, 3, 4, 5, 5, 5, 6, 7, 7, 8, 9 4 0, 0, 0, 1, 2, 3, 6, 8 5 0, 0 TABULAR METHOD By organizing graphs into tables, important features about the data can be readily available and comparison can be easily done. TABULAR METHOD A frequency distribution table is a table which shows the data arranged into different classes and the number of cases which fall into each class. A frequency distribution is a grouping of data into categories, showing the number of observations (frequency) in each non-overlapping classes. The grouping is usually constructed in a table.  Table Number Table Title Column Header Row Classifier Body Source Note GRAPHICAL METHOD Graphical presentation of data easier to comprehend in terms of the trend of the data. Other than that it adds aesthetic and life but more interestingly, it helps facilitate comparison and interpretation without going through the numerical data. GRAPHICAL METHOD ▪ Bar Chart (Vertical and Horizontal) ▪ Histogram ▪ Frequency Polygon ▪ Pie/Circle Graph ▪ Ogive GRAPHICAL METHOD ▪ Bar Chart (Vertical and Horizontal) A bar chart is a graph presented by either vertical or horizontal rectangles whose bases represents the class intervals and whose heights represents the frequencies. GRAPHICAL METHOD: BAR GRAPH ▪ Example: GRAPHICAL METHOD: BAR GRAPH GRAPHICAL METHOD: BAR GRAPH GRAPHICAL METHOD ▪ Histogram A histogram is a graph represented by vertical or horizontal rectangles whose bases are class marks and whose heights are the frequencies. GRAPHICAL METHOD: HISTOGRAM ▪ Example: GRAPHICAL METHOD: HISTOGRAM GRAPHICAL METHOD ▪ Frequency Polygon A frequency polygon is a line graph whose bases are the class marks and whose heights are the frequencies. GRAPHICAL METHOD: FREQUENCY POLYGON ▪ Example: GRAPHICAL METHOD: FREQUENCY POLYGON GRAPHICAL METHOD ▪ Pie/Circle Graph A pie chart is a circle graph showing the proportion of each class through either the relative or percentage frequency. GRAPHICAL METHOD: PIE GRAPH GRAPHICAL METHOD: PIE GRAPH GRAPHICAL METHOD: PIE GRAPH ▪ Example: GRAPHICAL METHOD: PIE GRAPH GRAPHICAL METHOD ▪ Ogive A ogive is a line graph where the bases are the class boundaries and the heights are the less than cumulative frequency (< 𝑐𝑓) for the less than ogive and the (> 𝑐𝑓). GRAPHICAL METHOD: OGIVE ▪ Example: GRAPHICAL METHOD: OGIVE GRAPHICAL METHOD: OGIVE