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‘ MODULE -41: FOUNDATION OF STATISTICS } INTRODUCTION TO STATISTICS « Statistics is the science of collecting , organizing , analyzing , interpreting and presenting data. * It helps us to take better decisions in daily life. e It deals with numbers as well as facts. e It ts used in every field - Business, Science, Education, Sports, Medicine, Government, etc. a APUSES| OF STATISTICS aaa 2aseeue oe = al & © & wg Business Science Education Sports Medicine Government KEY STATISTICAL TERMS Term Meaning Data Row facts and figures collected. Information Processed data which gives meaning . Observation Each item or value collected. Variable A characteristic which can change . Dataset A collection of data. Population The whole. group of items or people. Sample A part of the population. Parameter A number that describes a population. Stotistic A number that describes a sample. POPULATION AND SAMPLE © Population: The entire group of people or things we want to study - Example: All students in a college. ¢ Sample: A small part of the population chosen for study . Example: 100 students selected from the college. a ae eine ee = eee -{ POPULATION vs SAMPLE }-~----—~~ A | ———$———————— | | Population Sample | | Fi | | Whole group Part of the group | Large in size Small in size Costly and time taking Cheaper and faster Example: ALL voters Example: 500 voters ; at a ee ee ee Ee 4. TYPES OF DATA QUALITATIVE (Categorical) QUANTITATIVE (Numerical) NOMINAL (No order) Example : Blood group, Gender, Color ORDINAL (Has order) Example : Rank, Class, Education level DISCRETE (Countable) Example : No. of students, No. of cars LYS CONTINUOUS (Measurable) Example : Height, Weight, Time, Temperature 5. VARIABLES * Variable is a characteristic or quality that can change. * Types of Variables: — Independent Variable : The one we change. (Example : Study hours) - Dependent Variable : The one we measure. (Exomple : Marks) - Control Variable: The one we keep same. (Example: Same teacher) Flow: Change in Independent Voriable —> affects Dependent Variable | e 6. MEASUREMENT SCALES Scale Description Example Properties / Operations Nominal Names or categories Blood. group, We can only classify. without any order. Religion, Color a: Ordinal Order or ranking dst, and, 3rd We can compare. is present. Good, Better, Best S 4p 2 Ss Interval Ordered with equal Temperature (°C,*F) | We can add or subtract. difference between values. Calendar years ae eo (No true zero) Ratio Ordered with equal Height, Weight, All arithmetic operations difference and true zero. Time, Income (+,-,%, +) possible. L - 7. DATA COLLECTION METHODS DATA COLLECTION METHODS v Survey Interview Questionnaire Observation Experiment Secondary Date (Asking (Talking to (Written (Watching (Doing a (From books, questions) people) questions) carefully) test) internet, records aplag ee ee ee Se a oe, Sh, -@) | Note i * Primary data: Collected by us for the first time. \ i . Secondary dota: Already collected by someone else. i) 24. SAMPLING TECHNIQUES (Detoil) SAMPLING TECHNIQUES Y 4 Y Y r \ F -) ae =. 4 4, Simple Random 2. Systematic 3. Stratified 4, Cluster 5. Convenience Sampling Sampling Sampling Sampling Sampling * Every member has * Select every kt + Divide population * Divide population + Select members equal chance. item from o list into groups into clusters. who are easily © Each item is « First item ts (Strata) . 5 Siiecd some available . selected purely chosen vandomly. «Then take sample dusters and take * Quick ond easy by chance. from each group. items in them. but less accurate. Example: Example: Example: Example: Example: Drawing names Every 10% house Boys and Girls Some schools Asking friends in box. i treet . elected ’ selected ity. the class. | from 0 box J (in a stree J separately from city. J 25. ADVANTAGES AND DISADVANTAGES f XY ig Method. Advantages Disadvantages eee Census + More accurate + Costly [* Use Census when — | * No sampling error * Takes more time | population is small. | * Complete information + Not posstble for large population | | 4 Use Sampling when | Sompling + Less costly Less accurate than census | population is large. | + Saves time Sampling error may occur Wa ees Gach, Serres { * Easy to do Needs proper sampling method | = a ' Good Sampling | * Gives velioble vesults Wrong sampling gives wrong results and reliable results. { * Represents whole population | + Needs skill and planning | © { * Saves resources } 26. ERRORS IN STATISTICS 2%. CHARACTERISTICS OF GOOD STATISTICS * Human Error: Mistakes while collecting or 4. Tt should be based on facts. recording date. 2. Te should be collected for a definite purpose. * Sampling Error: Difference between sample 3. Te should be accurate and reliable. eee et eel perishes el 4. Tk should be collected in a proper way. % TNenstormeling| Egor!) (Dlstakss idue: to, rong 5. Tt should be simple and easy to understand . tools, wrong method, non-response etc. 6. It should be placed in a proper order. ° Th be reduced 5 iptadins ag ee Ee ah 7. Tk should be useful for decision making. training and careful work. Helps in decision making Questionnaire, Observation, pS fields of life Experiment, Secondary data. ----------------------------- ----- ----- +--+ a { MIND MAP (Quick View) | I i a ee ~ | De | KEY FORMULA | I Facts and figures T eetiaat | | | (Types: Qualitative, | | Percentage = Part git | | | Whole Hl FOUNDATION | | Example 1 i OF STATISTICS | | Tf 25 students out of 1 H | | 400 passed the test. | | | H - | | Pircintage = 28 x400 | rT Data Caen Use of Statistics | | 100 | i Survey, Interview, i | = 25% i 1 eae | | ae | | i | i) 4 ) 19. DATA PRESENTATION « After collecting dato, we present it in oa simple and clear form. { FORMS OF DATA PRESENTATION } v v Diagrammatic Graphical Presentation Presentation (Using pictures) (Using graphs) Example: Example: Bor chert, Line graph, Pie chart Histogram pcrcntn-n-=-------- 20. TYPES OF GRAPHS (With Use) | EXAMPLE: PIE CHART arias = | Favourite Graph Use Exomple 1 Bae Bor Graph To compare data between | Sales of two different | different groups. shops. | Line Groph | To show change over time. | Temperature change | over a week. Pie Chart To show parts of a whole | Market share of | in percentage. different companies. | Histogram To show frequency distribution | Marks of students | - of continuous data. in a test. | [Total = 100% | | { 24. FREQUENCY DISTRIBUTION (Basic) . Te shows how many times each value occurs in the dota. {CAL parts make a whole) | 22. CENTRAL TENDENCY (Very Basic Idea) + Tt tells us the central or typical value of the dota. + Ik is shown in a frequency table. Central Tendency Example: Marks of 10 students in a test 7 iS, Fe Be Bats Ge 4, Sy Bae Mean (Average) Median (Middle Value) Mode (Most Common Value) Add all values Arrange in order The value that Marks Tally Morks | Frequency (No. of Students) and divide by ond pick the occurs most = Th a total number. middle one. frequently . & ! é 23. RELATION BETWEEN VARIABLES Z mn 2 * Two variables can be related to each other. 8 4 2 T 1 q 1 4 Positive Relation Negative Relation No Relation When one increases, | |} When one increases, No clear pattern Total 10 the other also the other decreases. between variables. therenses. Example: Price of a Example: Shoe size Example® Study product and demand. and. intelligence . hours and marks + Statistics is the science of collecting, organizing, analyzing and presenting data. * Data can be qualitative or quantitative. * Variables can change. * Data is collected by different methods. + Data can be presented in tables, charts and graphs. QUICK REVISION * Census studies all members; sompling studies some members. * Good sampling gives goed results + Statistics helps in decision making. * It is used in business, science, education, medicine, sports, government and many more fields. 28 . NUMERICAL EXAMPLES Example 4: Dota and Variable © A teacher recorded the marks of 8 students. Dota: 45, 52, 61, 38, 55, 47, 66, 50 . Variable: Marks (Quantitative) , Type: Discrete (whole numbers) Example 2: Quolitative Data * Colors of 10 cars in a parking lot. Deta: Red, White, Black, Red, Blue, White, Black, Silver, Red, Blue 29. CONSTRUCTION OF FREQUENCY TABLE Example: Marks of 12 students 5, 7, 8, 6, 7,9, 5,8, 6, 7, 8,49 Marks Tally Marks Frequency (No. of Students) 5 W 2 6 MW 2 7 HL 3 8 tL 3 is | i 2 Total 42 Population is whole group and sample is part of it. medicine, sports, government and many fields. Lee \ * Variable: Color (Qualitative) “| Tally Morks: Count using | Types Nomina Oe Sg AN 2) 30. GRAPHICAL REPRESENTATION EXAMPLES Bar Graph Line Graph Pie Chart Histogram No. of Tamp (°C) Freq. ee - ‘6 3 25 4 ald Py ° Z Z Z ° 5 6 8 4 2 Ha he Wad a 0-10 10-20 20-30 30-40 40-50 ees Days Class Interval 31. PRACTICAL APPLICATION EXAMPLES 32. QUICK DIFFERENCE + Business: To know profit, loss, sales and market trend. Basis Descriptive Statistics | Inferential Statistics f bs Meant Describes the data Makes or Gove t: Census, » tox, » policies. anny — iia aie ca sabia: peers we have. prediction . + Education: Result analysis, performance improvement . is Wa TMs Te ea rE © Medicine: Drug tests, patient reports, health surveys. only . conclude population © Science: Experiments, research data, discoveries. Example Mean, Median, Graph. | Estimation, Hypothesis testing . Sports: rormance, records, selection. : Pager Fe 7 Purpose | To organize and Te drow conclusion summarize dota. about population 33. IMPORTANT FORMULAS (Basics) 4. Percentage po te eg } 3. Relative Frequency i 4. Range \ | | | Percentage = P&E 400 | Mean = Some of all Seales: eins agency © eee Range = Highest value | le wat | Total number of values | Total Frequency Pare nr xample: | i ¥ | Tf 18 out of GO students | a i foe Example: 1 | passed the exam ' 0 iiey Sp eat | eveaies Deta: 3, 7,9, 2,5 18 ! At6+8+10+42 i Totel = 45 Percentage = —— x 100 | ag i Ronge = 9-2 = # | H | | ! : fi ARY (ONE LINE | v Statistics is the science of data. ¥ Data is presented in tables, charts and graphs. | ¥ Data can be qualitative or quantitative ¥ Good sampling gives good ond reliable results. | aa Netebash: come leclapencngs apendient jer. corral ¥ Statistics helps in decision making . | ¥ Data te collected by different methods. v It is used in business, science, education, tv i L# Census studies all; sompling studies some. ¥ Proper steps lead to correct results. 34. 35. 36. KEY TAKEAWAYS FROM MODULE 1 Statistics is all about date. Collect good data for good results. Understand the population and sample. Use proper methods and steps. Present data in a clear and simple wo Analyze corefully and drow the right conclusion. Statistics helps in real life in many ways. SUMMARY TABLE : FOUNDATION OF STATISTICS (Quick Review) Concept Meaning Examples Key Points Data. Facts and figures Marks of students , Can be qualitative or collected Retell, (es quantitative Votes in election Variable A. characteristic Height, Age, Weight, Con be independent, that can change. Coler, Income. dependent or control. Population Complete group ALL students in a school, | Large in size. under study ALL people ina city Sample Part of the population 100 students from Smaller in size. selected. the school. Dota Collection Process of collecting Survey Interview , Use proper methods data Questionnaire, Observation . Presentation Showing date. in Bar groph, Pie chart, Makes dato easy tables, charts, graphs Line graph, Table to understand Analysis Studying data using Mean, Medion, Mode, Helps in finding teols and methods Range , Percentage. useful information . Interpretation Finding meaning and Result of o test, Leads to decision drawing conclusion Sales trend, ete making COMMON MISTAKES TO AVOID Collecting incomplete or wrong data. Using wrong method fer data collection. Taking small sample for large population Not organizing data properly. Wrong calculations . Drawing conclusion without full analysis Ignoring important facts. PRACTICE QUESTIONS . Give two examples of qualitative data . Give two examples of quantitative date. . What is a sample? Write any four methods of data collection . Differentiate between census and sampling. . What is the use of bar graph? + 2 3 4. What is a population? 5 6 ¥ 8 37. SELF CHECK (YES / NO) ene nrone 4. What is mean 10. What is median? 41. What is mode? \ 1 1 1 | 412. Write the for e. formula for percentag | 43. HAG oie of hes pasate) ! | | ! | 1 ! find the percentage 14. List any four applications of si 15. Why is proper data collection important? Do I know what statistics is? Can I differentiate between population and sample? Do I know different types of data? Can I name methods of data collection? Do I know how to present data in graphs? Can I calculate percentage, mean and range? Do I know steps in a statistical study? Can I give veal life examples of statistics? tistics. - Survey, Interview 5 Questionnaire , Experiment %. Census: All members Some members. 44. TYPES OF VARIABLES 45. SCALES OF MEASUREMENT Type Description Examples Noture Scale Description Example 41. Qualitative | Describe quolities or | © Gender Non-numerical 4 Newinel Dota ore classified into | Blood group (Categorieal) | categories. Cannot * Blood Group (Nominal or Ordinal) Scull categories. No order (A, B, AB, 0) be measured in © Type of fruit numerical terms * Eye color 2. Ordinel, Dea have a meaningful | Class ronk ing but Te = Fi = Scale oe (ast, 2nd, 3rd) (Discrete) Whole numbers, + Number of cars | (Countable) . obtained by courting. | + Number of books 3. Interval, Ordered date swith Temperature 3. Quantitative Measurable values. © Height Numerical Scala equel intervals. (in °C or °F) (Continuous) Con take any value © Weight (Messurable) No true zero within . wokure ve lee 4. Ratio Ordered date with Height, Weight, + Tune Seale equol. intervals. Age, Income Has o true zero. 46. FREQUENCY DISTRIBUTION TABLE - EXAMPLE HOW TO READ A TABLE © Read the title carefully f \ Example: Morks obtained by 20 students in o test | | | 1 | Check what each column represents. | | | | i | | | 5,7, 6,8, 4%,9,6,5, 8, 7,6,9, 8 #,5, 6,9, 8, 7,6 Marks. Tally Marks Frequency (No. of Students) | Relative Frequency * [Look ot the units (if ony) 5 Ht Py 3/20 = 0.45 * Compare the values a 6 @/20 = 0.30 = ee eee gee © 3 HH Ill 6 6/20 = 0.30 8 wi 4 4/20 = 0.20 4 Ml 3 3/20 = 0.45 Total 20 1.00 (100%) 4%. GRAPHICAL PRESENTATION - EXAMPLES 1. Bar Graph 2. Line Graph 3. Pie Chart Temp (°C) iy 35 y A. 25 rs g FA Education & elage tao ne | Rae mee 20% 0 G40 10°20 2030 30-40 40-50 Subjects Days Class Interval 48. STEPS IN STATISTICAL STUDY 44. IMPORTANCE OF STATISTICS Saves time and money Reduces confusion and guesswork Provides accurate ond reliable information Useful in business, industry, science, education, medicine, government ond daily life. Helps in comparison and evaluation. Aids in planning for the future REAL LIFE APPLICATIONS [inl] Sasiness ~ Sales, Profit, Loss JB Educotion - Results, Anolysis JET Goermnent = Census, Parning OF) Agriulture = Crop Yield QD Maticine = Patient Date. [E] Sets = Pedomance Aras \ as stp Petter Dees, Setar Payee Better Decisions -> Better Future 
