Mean Deviation

Statistics – Mean Deviation ”; Previous Next Referred to as average deviation, it is defined as the sum of the deviations(ignoring signs) from an average divided by the number of items in a distribution The average can be mean, median or mode. Theoretically median is d best average of choice because sum of deviations from median is minimum, provided signs are ignored. However, practically speaking, arithmetic mean is the most commonly used average for calculating mean deviation and is denoted by the symbol ${MD}$. We”re going to discuss methods to compute the Mean Deviation for three types of series: Individual Data Series Discrete Data Series Continuous Data Series Individual Data Series When data is given on individual basis. Following is an example of individual series: Items 5 10 20 30 40 50 60 70 Discrete Data Series When data is given alongwith their frequencies. Following is an example of discrete series: Items 5 10 20 30 40 50 60 70 Frequency 2 5 1 3 12 0 5 7 Continuous Data Series When data is given based on ranges alongwith their frequencies. Following is an example of continous series: Items 0-5 5-10 10-20 20-30 30-40 Frequency 2 5 1 3 12 Print Page Previous Next Advertisements ”;

Quadratic Regression Equation

Statistics – Quadratic Regression Equation ”; Previous Next Quadratic regression is deployed to figure out an equation of the parabola which can best fit the given set of data. It is of following form: ${ y = ax^2 + bx + c where a ne 0}$ Least square method can be used to find out the Quadratic Regression Equation. In this method, we find out the value of a, b and c so that squared vertical distance between each given point (${x_i, y_i}$) and the parabola equation (${ y = ax^2 + bx + c}$) is minimal. The matrix equation for the parabolic curve is given by: $ {begin{bmatrix} sum {x_i}^4 & sum {x_i}^3 & sum {x_i}^2 \ sum {x_i}^3 & sum {x_i}^2 & sum x_i \ sum {x_i}^2 & sum x_i & n end{bmatrix} begin{bmatrix} a \ b \ c end{bmatrix} = begin{bmatrix} sum {x_i}^2{y_i} \ sum x_iy_i \ sum y_i end{bmatrix} }$ Correlation Coefficient, r Correlation coefficient, r determines how good a quardratic equation can fit the given data. If r is close to 1 then it is good fit. r can be computed by following formula. ${ r = 1 – frac{SSE}{SST} where \[7pt] SSE = sum (y_i – a{x_i}^2 – bx_i – c)^2 \[7pt] SST = sum (y_i – bar y)^2 }$ Generally, quadratic regression calculators are used to compute the quadratic regression equation. Example Problem Statement: Compute the quadratic regression equation of following data. Check its best fitness. x -3 -2 -1 0 1 2 3 y 7.5 3 0.5 1 3 6 14 Solution: Compute a quadratic regression on calculator by putting the x and y values. The best fit quadratic equation for above points comes as ${ y = 1.1071x^2 + x + 0.5714 }$ To check the best fitness, plot the graph. So the value of Correlation Coefficient, r for the data is 0.99420 and is close to 1. Hence quadratic regression equation is best fit. Print Page Previous Next Advertisements ”;

Tableau – Rename Worksheet

Tableau – Rename Worksheet ”; Previous Next You can give appropriate names to the existing worksheets by renaming a worksheet. This helps in relating the content of the worksheet with its name. For example, if we want to know which sheet has the view to know the segment wise profit then with a proper name of the sheet we can identify it. Renaming the Worksheet To rename a worksheet, right-click the sheet name and choose the option Rename Sheet. The following diagram shows the worksheet with the new name. Print Page Previous Next Advertisements ”;

Normal Distribution

Statistics – Normal Distribution ”; Previous Next A normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme. Height is one simple example of something that follows a normal distribution pattern: Most people are of average height the numbers of people that are taller and shorter than average are fairly equal and a very small (and still roughly equivalent) number of people are either extremely tall or extremely short.Here”s an example of a normal distribution curve: A graphical representation of a normal distribution is sometimes called a bell curve because of its flared shape. The precise shape can vary according to the distribution of the population but the peak is always in the middle and the curve is always symmetrical. In a normal distribution the mean mode and median are all the same. Formula ${y = frac{1}{sqrt {2 pi}}e^{frac{-(x – mu)^2}{2 sigma}} }$ Where − ${mu}$ = Mean ${sigma}$ = Standard Deviation ${pi approx 3.14159}$ ${e approx 2.71828}$ Example Problem Statement: A survey of daily travel time had these results (in minutes): 26 33 65 28 34 55 25 44 50 36 26 37 43 62 35 38 45 32 28 34 The Mean is 38.8 minutes, and the Standard Deviation is 11.4 minutes. Convert the values to z – scores and prepare the Normal Distribution Graph. Solution: The formula for z-score that we have been using: ${z = frac{x – mu}{sigma} }$ Where − ${z}$ = the “z-score” (Standard Score) ${x}$ = the value to be standardized ${mu}$ = mean ${sigma}$ = the standard deviation To convert 26: First subtract the mean: 26-38.8 = -12.8, Then divide by the Standard Deviation: -12.8/11.4 = -1.12 So 26 is -1.12 Standard Deviation from the Mean Here are the first three conversions. Original Value Calculation Standard Score (z-score) 26 (26-38.8) / 11.4 = -1.12 33 (33-38.8) / 11.4 = -0.51 65 (65-38.8) / 11.4 = -2.30 … … … And here they graphically represent: Print Page Previous Next Advertisements ”; Tutorials Point is a leading Ed Tech company striving to provide the best learning material on technical and non-technical subjects. About us Company Our Team Careers Jobs Contact Us Terms of use Privacy Policy Refund Policy Cookies Policy FAQ”s Tutorials Point India Private Limited, Incor9 Building, Kavuri Hills, Madhapur, Hyderabad, Telangana – 500081, INDIA Tutorials Articles Jobs Courses Certifications Annual Membership Languages Python Tutorial Java Tutorial C++ Tutorial C Programming Tutorial C# Tutorial PHP Tutorial R Tutorial Go Tutorial Web Technologies HTML Tutorial CSS Tutorial JavaScript Tutorial ReactJS Tutorial Bootstrap Tutorial AngularJS Tutorial Node.js Tutorial TypeScript Tutorial Database SQL Tutorial MySQL Tutorial DBMS Tutorial MongoDB Tutorial SQLite Tutorial PL/SQL Tutorial PostgreSQL Tutorial Excel Tutorial Editors Online SQL Editor Online Html Editor Online Css Editor Online Javascript Editor Online Latext Editor Online TEX Editor Online Mathml Compiler Online Markdown Editor Trending Technologies Cloud Computing Tutorial Amazon Web Services Tutorial Microsoft Azure Tutorial Git Tutorial Ethical Hacking Tutorial Docker Tutorial Kubernetes Tutorial Compilers Online Java Compiler Online C Compiler Online C++ Compiler Online C# Compiler Online Php Compiler Online Matlab Compiler Online Bash Compiler Terminals Online Unix Terminal Online Python3 Terminal Online Php Terminal Online Nodejs Terminal Online R Terminal Online Numpy Terminal Online Octave Terminal Data Science & ML NLP Tutorial NumPy Tutorial Python Pandas Tutorial Machine Learning Tutorial Big Data Analytics Tutorial Cryptography Tutorial Power BI Tutorial Computer Science DSA Tutorial Spring Boot Tutorial SDLC Tutorial Unix Tutorial Operating System Tutorial Assembly Programming Tutorial Digital Circuits Tutorial Microprocessor Tutorial System Analysis and Design Tutorial Flutter Tutorial Top Certifications Business Analytics Certification Java & Spring Boot Advanced Certification Data Science Advanced Certification Advanced Certification In Cloud Computing And DevOps Advanced Certification In Business Analytics Artificial Intelligence And Machine Learning Certification DevOps Certification   Game Development Certification Front-End Developer Certification AWS Certification Training Python Programming Certification Generative AI Certification Microsoft Excel Certification Training Java Certification Cyber Security Certification Coding For Beginners Certification   JavaScript Certification Apache Spark Certification Advanced Python Certification Back-End Developer Certification Front-End Developer Certification Web Developer Advanced Certification Linux System Administrator Certification Automation Testing Certification Training © Copyright 2024. All Rights Reserved.

Tableau – LOD Expressions

Tableau – LOD Expressions ”; Previous Next Level of Detail (LOD) expressions are used to run complex queries involving many dimensions at the data source level instead of bringing all the data to Tableau interface. A simple example is adding dimension to an already calculated aggregate value. Types of LOD There are three main types of LOD expressions. FIXED LOD This expression computes values using the specified dimensions without reference to any other dimensions in the view. INCLUDE LOD This level of detail expressions compute values using the specified dimensions in addition to whatever dimensions are in the view. EXCLUDE LOD These levels of detail expressions subtract dimensions from the view level of detail. FIXED Level of Detail Expressions Find the amount of Sales for each state in each region. Here, first create the formula field named Regional Sales using the formula as shown in the following screenshot. Next, drag the Region and State field to the Rows shelf and the calculated field to the Text shelf under the Marks card. Also drag the Region field to the Color shelf. This produces the following view, which shows a fixed value for different states. That is because we have fixed the dimension as region for the calculation of Sales value. INCLUDE Level of Detail Expressions INCLUDE level of detail expressions compute values using the specified dimensions in addition to whatever dimensions are in the view. Calculate the sum of sales per state for each sub-category of products. For this, drag the Sub-Category field to the Rows shelf. Then, write the expression in the Columns shelf as shown in the following screenshot. It produces the following view which includes both the dimensions in the calculations. EXCLUDE Level of Detail Expressions EXCLUDE level of detail expressions specify dimensions to exclude from the view level of detail. Exclude Region from Sales figure calculated for every month. Create the formula as shown in the following screenshot. On dragging the relevant fields to the respective shelves, you will get the final view for the EXCLUDE LOD as shown in the following screenshot. Print Page Previous Next Advertisements ”;

Log Gamma Distribution

Statistics – Log Gamma Distribution ”; Previous Next Log Gamma Distribution is a probability density function with positive shape parameters $ {alpha, beta } $ and location parameter $ { mu } $. It is defined by following formula. Formula ${ f(x) = frac{e^{beta x}e^{frac{-e^x}{alpha}}}{ alpha^beta Gamma(beta)} \[7pt] , where -infty gt x lt infty }$ Where − ${alpha}$ = positive shape parameter. ${beta}$ = positive shape parameter. ${x}$ = random variable. Following diagram shows the probability density function with three different parameter combinations. Print Page Previous Next Advertisements ”;

Tableau – Reorder Worksheet

Tableau – Reorder Worksheet ”; Previous Next Sometimes you need to change the position of the existing worksheet to study them in a better way. This can be done in a simple way by dragging the sheet name from its existing position to the new position. Reordering the Worksheet To reorder a worksheet, click and hold the worksheet name and move it to the desired position. Consider the three worksheets as shown in the following screenshot. The following screenshot shows that a vertical dark line appears in the new position on dragging the third worksheet from left to the new position. Print Page Previous Next Advertisements ”;

Probability Multiplecative Theorem

Statistics – Probability Multiplicative Theorem ”; Previous Next For Independent Events The theorem states that the probability of the simultaneous occurrence of two events that are independent is given by the product of their individual probabilities. ${P(A and B) = P(A) times P(B) \[7pt] P (AB) = P(A) times P(B)}$ The theorem can he extended to three or more independent events also as ${P(A cap B cap C) = P(A) times P(B) times P(C) P (A,B and C) = P(A) times P(B) times P(C) }$ Example Problem Statement: A college has to appoint a lecturer who must be B.Com., MBA, and Ph. D, the probability of which is ${frac{1}{20}}$, ${frac{1}{25}}$, and ${frac{1}{40}}$ respectively. Find the probability of getting such a person to be appointed by the college. Solution: Probability of a person being a B.Com.P(A) =${frac{1}{20}}$ Probability of a person being a MBA P(B) = ${frac{1}{25}}$ Probability of a person being a Ph.D P(C) =${frac{1}{40}}$ Using multiplicative theorem for independent events ${ P (A,B and C) = P(A) times P(B) times P(C) \[7pt] = frac{1}{20} times frac{1}{25} times frac{1}{40} \[7pt] = .05 times .04 times .025 \[7pt] = .00005 }$ For Dependent Events (Conditional Probability) As defined earlier, dependent events are those were the occurrences or nonoccurrence of one event effects the outcome of next event. For such events the earlier stated multiplicative theorem is not applicable. The probability associated with such events is called as conditional probability and is given by P(A/B) = ${frac{P(AB)}{P(B)}}$ or ${frac{P(A cap B)}{P(B)}}$ Read P(A/B) as the probability of occurrence of event A when event B has already occurred. Similarly the conditional probability of B given A is P(B/A) = ${frac{P(AB)}{P(A)}}$ or ${frac{P(A cap B)}{P(A)}}$ Example Problem Statement: A coin is tossed 2 times. The toss resulted in one head and one tail. What is the probability that the first throw resulted in a tail? Solution: The sample space of a coin tossed two times is given as S = {HH, HT, TH, TT} Let Event A be the first throw resulting in a tail. Event B be that one tail and one head occurred. ${ P(A) = frac{P(TH,TT)}{P(HH,HT,TH,TT)} = frac{2}{4} =frac {1}{2} \[7pt] P(A cap B) = frac{P(TH)}{P(HH,HT,TH,TT)} =frac{1}{4} \[7pt] So P (A/B) = frac{P(A cap B)}{P(A)} \[7pt] = frac{frac{1}{4}}{frac{1}{2}} \[7pt] = frac{1}{2} = 0.5 }$ Print Page Previous Next Advertisements ”;

Tableau – Operators

Tableau – Operators ”; Previous Next An operator is a symbol that tells the compiler to perform specific mathematical or logical manipulations. Tableau has a number of operators used to create calculated fields and formulas. Following are the details of the operators that are available and the order (precedence) of operations. Types of Operator General Operators Arithmetic Operators Relational Operators Logical Operators General Operators Following table shows the general operators supported by Tableau. These operators act on numeric, character, and date data types. Operator Description Example +(addition) Adds two numbers. Concatenates two strings. Adds days to dates. 7 + 3 Profit + Sales ”abc” + ”def” = ”abcdef” #April 15, 2004# + 15 = #April 30, 2004# –(subtraction) Subtracts two numbers. Subtracts days from dates. -(7+3) = -10 #April 16, 2004# – 15 = #April 1, 2004# Arithmetic Operators Following table shows the arithmetic operators supported by Tableau. These operators act only on numeric data types. Operator Description Example *(Multiplication) Numeric multiplication 23*2 = 46 /(Division) Numeric division 45/2 = 22.5 %(modulo) Reminder of numeric division 13 % 2 = 1 ^(power) Raised to the power 2^3 = 8 Comparison Operators Following table lists the comparison operators supported by Tableau. These operators are used in expressions. Each operator compares two numbers, dates, or strings and returns a Boolean (TRUE or FALSE). Booleans themselves, however, cannot be compared using these operators. Operator Description Example = = or = (Equal to) Compares two numbers or two strings or two dates to be equal. Returns the Boolean value TRUE if they are, else returns false. ‘Hello’ = ‘Hello’ 5 = 15/ 3 != or <> (Not equal to) Compares two numbers or two strings or two dates to be unequal. Returns the Boolean value TRUE if they are, else returns false. ‘Good’ <> ‘Bad’ 18 != 37 / 2 > (Greater than) Compares two numbers or two strings or two dates where the first argument is greater than second. Returns the boolean value TRUE if it is the case, else returns false. [Profit] > 20000 [Category] > ‘Q’ [Ship date] > #April 1, 2004# < (Less than) Compares two numbers or two strings or two dates where the first argument is smaller than second. Returns the boolean value TRUE if it is the case, else returns false. [Profit] < 20000 [Category] < ‘Q’ [Ship date] < #April 1, 2004# Logical Operators Following table shows the logical operators supported by Tableau. These operators are used in expressions whose result is a Boolean giving the output as TRUE or FALSE. Operator Description Example AND If the expressions or Boolean values present on both sides of AND operator is evaluated to be TRUE, then the result is TRUE. Else the result is FALSE. [Ship Date] > #April 1, 2012# AND [Profit] > 10000 OR If any one or both of the expressions or Boolean values present on both sides of AND operator is evaluated to be TRUE, then the result is TRUE. Else the result is FALSE. [Ship Date] > #April 1, 2012# OR [Profit] > 10000 NOT This operator negates the Boolean value of the expression present after it. NOT [Ship Date] > #April 1, 2012# Operator Precedence The following table describes the order in which operators are evaluated. The top row has the highest precedence. Operators on the same row have the same precedence. If two operators have the same precedence, they are evaluated from left to right in the formula. Also parentheses can be used. The inner parentheses are evaluated before the outer parentheses. Precedence Operator 1 –(negate) 2 ^(power) 3 *, /, % 4 +, – 5 ==, >, <, >=, <=, != 6 NOT 7 AND 8 OR Print Page Previous Next Advertisements ”;

Qualitative Data Vs Quantitative Data

Statistics – Qualitative Data Vs Quantitative Data ”; Previous Next Qualitative Data Qualitative data is a set of information which can not be measured using numbers. It generally consist of words, subjective narratives. Result of an qualitative data analysis can come in form of highlighting key words, extracting information and concepts elaboration. For example, a study on parents perception about the current education system for their kids. The resulted information collected from them might be in narrative form and you need to deduce the analysis that they are satisfied, un-satisfied or need improvement in certain areas and so on. Strengh Better understanding – Qualitative data gives a better understanding of the perspectives and needs of participants. Provides Explaination – Qualitative data along with quantitative data can explain the result of the survey and can measure the correction of the quantitative data. Better Identification of behavior patterns – Qualitative data can provide detailed information which can prove itself useful in identification of behaviorial patterns. Weakness Lesser reachability – Being subjective in nature, small population is generally covered to represent the large population. Time Consuming – Qualitative data is time consuming as large data is to be understood. Possiblity of Bias – Being subjective analysis; evaluator bias is quite feasible. Quantitative Data Quantitative data is a set of numbers collected from a group of people and involves statistical analysis.For example if you conduct a satisfaction survey from participants and ask them to rate their experience on a scale of 1 to 5. You can collect the ratings and being numerical in nature, you will use statistical techniques to draw conclusions about participants satisfaction. Strengh Specific Quantitative data is clear and specific to the survey conducted. High ReliabilityIf collected properly, quantitative data is normally accurate and hence highly reliable. Easy communicationQuantitative data is easy to communicate and elaborate using charts, graphs etc. Existing supportMany large datasets may be already present that can be analyzed to check the relevance of the survey. Weakness Limited Options – Respondents are required to choose from limited options. High Complexity – Qualitative data may need complex procedures to get correct sample. Require Expertise – Analysis of qualitative data requires certain expertise in statistical analysis. Print Page Previous Next Advertisements ”;