Data Presentation- Tabulation PDF

Data Presentation- Tabulation Dr. Abdul-Sattar Nizami 1 Sustainable Development Study Centre (SDSC) Government College University, Lahore  Data Presentation Data Organization First task is to organize and simplify the data, so that it is...

Data Presentation- Tabulation Dr. Abdul-Sattar Nizami 1 Sustainable Development Study Centre (SDSC) Government College University, Lahore  Data Presentation Data Organization First task is to organize and simplify the data, so that it is possible to get a general overview of the results. Raw Data: Data that is not organized. Example: Survey Ungrouped Data: Data in its original form is called Ungrouped data. Note: Raw data is also called ungrouped data 2 Why and How Data Organization ? To understand data, it is organized and arranged in a meaningful form. This is done by the following ways. Classification – qualitative, quantitative, etc. Tabulation – simple, frequency, stem, leaf, etc. Graphs – bar, pie, charts, histogram, frequency, etc. 3 Data Classification The process of arranging data into homogenous group or classes according to some common characteristics present in the data is called data classification. 4 Data Classification / Organization…. Bases Types of Data of Data 5 Qualitative Base Quantitative Base Geographical Base Chronological or Temporal Base Bases of Data 6 Qualitative Base Examples: Religion, Gender, Color Quantitative Base Examples: Height, Age, Weight Geographical Base Examples: Location, States, Provinces, Cities Chronological or Temporal Base Examples: Time of Occurrence such as Years, Months, Weeks, Days, Time Series Data 7 Types of Data One Way Two Way Multi-way Class Class Class 8 One Way Class Single Characteristic. Example: World Population based on Religion Two Way Class 2 Characteristics. Example: World Population based on Religion and Gender Multi Way Class Multi Characteristics. Example: World Population based on Religion, Gender and Literacy 9 Tabulation of Data ▪ The process of placing classified data into tabular form is known as Tabulation. ▪ A Table is a symmetrical arrangement of statistical data into rows and columns. ▪ Rows are horizontal arrangement of data. ▪ Columns are vertical arrangement of data. 10 Simple or Double or One-Way Two-Way Table Table Complex or Multi-Way Table Types of Table 11 General Rules of Tabulation ▪ Table should be simple and attractive. ▪ A complex table should be divided/broken into relatively simple tables. ▪ Heading for columns and rows should be proper and clear. ▪ Suitable approximation may be adopted, and figures may be rounded off. However, this should be mentioned in the prefatory note or in the foot note. ▪ The unit of measurement and nature of data should be well defined. 12 Organizing Data via Frequency Tables ▪ One method for simplifying and organizing data is to construct a frequency distribution. ▪ Frequency Distribution: The organization of a set of data in a table showing the distribution of the data into classes or groups together with the number of observations in each class or group is called frequency distribution. ▪ Class Frequency: The number of observations falling in a particular class is called frequency or simply frequency, denoted by ‘f’. ▪ Group Data: Data presented in the form of a frequency distribution is called grouped data. 13 What is frequency distribution environmental statistics? Frequency distribution, in statistics, a graph or data set organized to show the frequency of occurrence of each possible outcome of a repeatable event observed many times. 14 FREQUENCY DISTRIBUTION Dr. Abdul-Sattar Nizami 15 Sustainable Development Study Centre (SDSC) Government College University, Lahore  Arrangement of data in a table in such a way that What is each class showing Frequency number of Distribution ? observations/frequency falling in that class. 16 Main Parts of Frequency Distribution ▪ Title – School/University Data ▪ Box head or Column Captions ▪ Stub or Row Captions ▪ Body of Data 17 Example Following data shows weight in pounds of 40 students at a College. Construct a frequency distribution Table using appropriate Class Intervals. 128, 150, 156, 145, 147, 165, 142, 140, 154, 135, 158, 118, 145, 146, 163, 161, 157, 180, 135, 149, 138, 140, 125, 126, 153, 144, 168, 135, 132, 144, 147, 150, 142, 164, 148, 173, 138, 136, 146 18 Example Weights in Pounds of Students Class No of Observations Tally 19 Example Class Intervals ? Range ? Number of Classes ? Class Intervals = Range / No of Classes 20  Range = Xm – Xo = 180 - 118 = 62 Example No of Classes = 1+ 3.322 log N = 1 + 3.322 log (39) = 6.32220 = 6.28 21 Example Class Intervals = Range / No of Classes = 62/7 = 9.87 = 9.9 = 10 22 Example Class No of Observations Tally 118-127 3 │││ 128-137 5 ││││ 138-147 9 148-157 12 158-167 5 168-177 4 178-187 2 23 Frequency Distribution of Qualitative Data Political Party Affiliations: ▪ Professor X asked his introductory statistics students to state their political affiliation as PML-N (N), PPP (P), PTI, and PML-Q (Q). ▪ The responses of the 30 students in a class are PPP, N, Q, PTI, N, Q, N, PPP, PTI, N, PTI, N, PTI, PPP, N, Q, N, PTI, Q, PTI, PPP, PTI, N, PTI, Q, PTI, N, PTI, Q, PPP Construct a frequency distribution ? 24 Party Frequency (f) Tally PTI 10 ││││││││ N 9 Q 6 P 5 Total 30 25 Interpretation Out of 30 students in the class, 10 are in favor of PTI 9 are in favor of PML-N 6 are in favor if PML-Q 5 are in favor of PPP 26  Relative Frequency Distribution Relative Frequency is the ratio of the frequency to the total number of observations. Relative frequency = Frequency / Number of observation Examples: Relative frequency of students who favored PTI = 10/30 = 0.333 = 33.33% Relative frequency of students who favored PML-N = 30% Relative frequency of students who favored PML-Q = 20% Relative frequency of students who favored PPP = 16.67% 27  Frequency Distribution of Qualitative Data Party Affiliation Example Party Frequency (f) Relative Freq PTI 10 10/30=0.3333 N 9 Q 6 P 5 Total 30 1 or 100% 28 Interpretation Out of 30 students in the class, 33.3% are in favor of PTI 30% are in favor of PML-N 20% are in favor if PML-Q 16.7% are in favor of PPP 29 The total frequency of a variable from its one end to a certain values (usually upper class boundary in grouped data), called the base. It is known as cumulative frequency less than or more than the base of the variable. Cumulative Frequency Distribution The table showing cumulative frequency is called cumulative frequency distribution. 30 Take difference of lower limit of second class and upper limit of first class. (e.g., 21-20=1). Then divide this difference by 2. (i.e., ½=0.5). Subtract the resulting number (i.e., 0.5) from lower class limit of each class and add the resulting number (i.e., 0.5) to the upper class limit of each class. The newly obtained classes are called Class Boundaries (C.B) Classes Class Frequency (f) Boundaries 11-20 10.5-20.5 3 21-30 20.5-30.5 6 31-40 30.5-40.5 5 41-50 40.5-50.5 4 51-60 50.5-60.5 2 Total 20 31 Less than Cumulative Frequency Distribution Classes Class Boundaries Frequency (f) 11-20 10.5-20.5 3 21-30 20.5-30.5 6 31-40 30.5-40.5 5 41-50 40.5-50.5 4 51-60 50.5-60.5 2 Total 20 Class Boundaries Cumulative Frequency Less than 10.5 0 Less than 20.5 3 Less than 30.5 3+6=9 Less than 40.5 9+5=14 Less than 50.5 14+4=18 32 Less than 60.5 18+2=20 More than Cumulative Frequency Distribution Classes Class Boundaries Frequency (f) 11-20 10.5-20.5 3 21-30 20.5-30.5 6 31-40 30.5-40.5 5 41-50 40.5-50.5 4 51-60 50.5-60.5 2 Total 20 Class Boundaries Cumulative Frequency More than 10.5 20 More than 20.5 20-3=17 More than 30.5 17-6=11 More than 40.5 11-5=6 More than 50.5 6-4=2 33 More than 60.5 2-2=0 Stem and Leaf Plot Disadvantage of Frequency Table An obvious disadvantage of using frequency table is that the identity of individual observation is lost in the grouping process. Stem and Leaf Plot provides the solution by offering a quick and clear way of sorting and displaying data simultaneously. 34 Method-Stem and Leaf Plot ▪ Sort the data series ▪ Separate the sorted data series into leading digits (the stems) and the trailing digits (the leaves). ▪ Example: In 13, the leading digit (stem) is 1 and trailing digit (leaf) is 3 and in 21, the leading digit (stem) is 2 and trailing digit (leaf) is 1. ▪ List all stems in a columns from low to high ▪ For each stem, list all associated leaves 35  Stem and Leaf Plot Example: Consider the temperature data The sorted data from low to high is shown below 12,13,17,21,24,24,26,27,27,30,32,35,37,38,41,43,44,46,53, 58 Here, use the 10’s digit for the stem unit. Stem Leaf 13 is shown as 1 3 21 is shown as 2 1 35 is shown as 3 5 36 Stem and Leaf Plot Data in ordered array 12,13,17,21,24,24,26,27,28,30,32,35,37,38,41,43,44,46,53, 58 Completed Stem-and-leaf diagram Stem Leaf 1 237 2 144678 3 02578 4 1346 5 38 37