Statistics Notes PDF

# Lec #1 Statistics & Probability ## Primary Data - 20 19 18 17 10 - 16 15 14 13 20 - 12 11 10 12 10 - 9 8 7 6 5 ## Types of Data ### Discrete Data - The whole number are called discrete. - Examples: Family Members and Countable, no of chair in class. ### Continuous Data ## Primary Data: (rea...

# Lec #1 Statistics & Probability ## Primary Data - 20 19 18 17 10 - 16 15 14 13 20 - 12 11 10 12 10 - 9 8 7 6 5 ## Types of Data ### Discrete Data - The whole number are called discrete. - Examples: Family Members and Countable, no of chair in class. ### Continuous Data ## Primary Data: (real-time data) - Primary data is information collected directly by someone for a specific purpose, like through surveys, interviews or experiments. - It's original and not taken from other sources. OR - The data which is collected/used for the very first time are called primary data. ## Secondary Data: (Past Data) - The data which is treated once is secondary data | Classes | F | Secondary Data | |--------------|---|-----------------| | 01 - 05 | 1 | | | 06 - 10 | 7 | | | 11 - 15 | 6 | | | 16 - 20 | 6 | | | | 20 | | ## Group Data - The data arrange in table in classified/specific form are called Group data. ## Ungroup Data - The data is not arrange in specific form are called ungroup data. ## Table - The combination of horizontal rows and vertical columns are called table. ## Tabulation - The process to put the data in the table are called tabulation. ## Classification - The process in which we arrange the data in tables are called classification. ## Frequency - The repeated number of data is called frequency. ## Statistics - Statistics is a science that deals with Collection, Presentation Analysis and Interpretation of data. ## Branches of Statistics ### Descriptive: - This type of statistic deals with the methods of drawing conclusion about population on the basis of limited information of sample. ### Inferentials: ## Population - A Sample population or a statistical population is a collection or set of all possible observations whether finite or infinite, relevant to some characteristics of interest. - It is denoted by uppercase letter "N". ## Sample - A Sample is a part, or a subset of a population. - Generally, it consists of some of the characteristics observations but in certain situations, it may include the whole of the population. - It is represented by the Symbol "n". # Lec #2 Statistics ## Qualitative Statistics: - The data which describe qualities/characteristics of an item. - It cannot be expressed in the form of numbers. - It is in the form of text, audio, video and images etc. - Examples: Honesty, Loyalty, Beauty, Colors and behaviors etc. ## Quantitative Statistics: - Data can be quantified, measured, or can assign a numerical value. - Examples: age, distance and income. ## Types of Quantitative Statistics ### Discrete: - Count - no. of family, no. of students, no. of Chairs ### Continuous: - Measure - scale (continuous) ## Attributes - Quality (non-measurable) Features - Like Beauty, Honesty ## Variables - Values Vary (Change) Measurable - Like Height #### MCQ'S: 36 students in class - a) variable - c) attributes #### (b) Numerical data #### (d) Quality data ## Class Boundary | Class Type I | Class Type II | Class Boundary (C.B.) | |--------------|----------------|------------------------| | 0 - 10 | 0 - 9 | 0.5 - 9.5 | | 10 - 20 | 10 - 19 | 9.5 - 19.5 | | 20 - 30 | 20 - 29 | 19.5 - 29.5 | | 30 - 40 | 30 - 39 | 29.5 - 39.5 | | 40 - 50 | 40 - 49 | 39.5 - 49.5 | | 50 - 60 | 50 - 59 | 49.5 - 59.5 | #### C B - class Type II say Banay gi class type #### 10 - 9 = 2 #### Say ni = 0.5 ## Mean/Average/Arithmetic Mean - Average = Sum of Values/No. of Values - Example: 886/20 = 44.3 - X = ΣX (Un Group data)/n - X = ΣFX (For Group data)/ΣF ## Find Arithmetic Mean? - Not required - Class Boundaries | Classes | F | X (Midpoint) | FX | |-------------------|------|----------------|-------------------| | 65 - 84 | 695 | 74.5 | 51,777.5 | | 85 - 104 | 947 | 94.5 | 89,491.5 | | 105 - 124 | 1919 | 114.5 | 219,725.5 | | 125 - 144 | 1325 | 134.5 | 178,212.5 | | 145 - 164 | 766 | 154.5 | 118,347 | | 165 - 184 | 716 | 174.5 | 124,942 | | 185 - 204 | 956 | 194.5 | 185,942 | | | 7324 | 941.5 | 968438 | - For Group data X= ΣFx/ΣF = 968438/7324 - X = 132.22 | Class | F | X | FX | |----------------|-----|--------|-------------| | 65 - 84 | 9 | 74.5 | 670.5 | | 85 - 104 | 10 | 94.5 | 945 | | 105-124 | 17 | 114.5 | 1946.5 | | 25 - 144 | 10 | 134.5 | 1345 | | 145 - 164 | 5 | 154.5 | 772.5 | | 165 - 184 | 4 | 174.5 | 698 | | 185 - 204 | 5 | 194.5 | 972.5 | | | 60 | | 7350 | - X = ΣFX/ΣF = 7350/60 = 122.5 ## Errors - Diff b/w Calculated & Actual Values ## How many ways to calculate primary and secondary data? - **Primary data** - Information collected from person - Questionaire - Form - Information through Enumerators - Local Sources - **Secondary data** - Offices - Semi-offices - Research paper - News Paper ## Types of Averages - Mean/A.M - G-M - H.M - Median - Mode ## Geometric Mean - nth root of product of the group n values is called Geometric Mean. - Un Group Data - G.M = (X₁*X₂*....*Xn)^1/n - Group Data - G.M= antilog (ΣFlogX/ΣF) ## Harmonic Mean - H.M is the reciprocal of the A.M of the reciprocal of the sum of the x values. - H.M = n/ Σ(1/x) (For Ungroup Data) - H.M = ΣF / ΣF (1/x) (For Group Data)