![Short Cut Method/ Indirect Method A.M.= A+ΣFdx/ΣF
Step-deviation Method A.M.=A+ΣFdx'/ΣF*i
Geometric Mean G.M.=√ab
Harmonic Mean
In Individual Series N/Σ(1/X)
In Discrete & Continuous series N/Σ(f*1/X)
Median
In Individual & Discrete Series M=N+1/2, (Nth term+N+1/2)/2
Continuous series N1=N/2, M=L+ N1-CF/F*i
Mode
In Individual Series Maximum repeated term
In Discrete & Continuous series Groupung Table & Analysis Table, M=
L+D1/(D1+D2)*i
Quartiles
In Individual & Discrete Series Q1=N+1/4, Q2=2(N+1)/4, Q3=3(N+1)/4
Continuous series N1=N/4, Q1=L+(N1-
C.F.)/F*i,N1=3N/4,Q3=L+(N1-C.F.)/F*i
Decile N1=N/10, D1=L+(N1-
C.F.)/F*i,N1=9N/10,D9=L+(N1-C.F.)/F*i
Percentile N1=10(N/100), P10=L+(N1-
C.F.)/F*i,N1=90N/100,P90=L+(N1-C.F.)/
F*i
Measures of dispersion
Range Highest Value-Lowest Value
Quartile Deviation Q3-Q1/2
Coeffcient of quartile deviation Q3-Q1/Q3+Q1
Mean Deviation
In Individual Series Σ[X-A.M.]/N
In Discrete & Continuous series ΣF[X-A.M.]/N
Coefficient Of Mean Deviation M.D./A.M.or M or Z
Standard Deviation
In Individual Series √Σd²/N-(Σd/N)2
In Discrete & Continuous series √Σfd²/N-(Σfd/N)2
Coefficient Of Standard Deviation S.D./A.M.
Variance S.D.²
Coefficient of variation S.D./A.M.*100
Coefficient Of Correlation
Karl Pearson r=NΣXY-(ΣX.ΣY)/√(NΣX²-
{ΣX}²).√(NΣY²-{ΣY}²)](https://image.slidesharecdn.com/module-100819042704-phpapp01/85/Module-7-320.jpg)
![Spearman 1-6ΣD²/N³-N When ranks are not
repeated
1-6[ΣD²+1/12{m³-m}]/N³-N, When ranks
are repeated
Concurrent deviation C √n (2C-n/n)
Standard Error 1-r²/√N
Probable Error 0.6745 (1-r²/√N)](https://image.slidesharecdn.com/module-100819042704-phpapp01/85/Module-8-320.jpg)
Module
- 1. Punjab College of Technical Education Ludhiana COURSE MODULE BUSINESS STATISTICS Name of Teacher: Asha Sharma (asha_s81@hotmail.com) Nidhi Juneja (nidhi_juneja30@yahoo.co.in) Subject Code: BB-304 No. Of lecture: 57 Class Tests: 2 Hourly test: 2 Assignment: 3 Activity: 2 Course Objective: Business Statistics is helpful in framing suitable policies in a large number of diversified fields covering natural, physical and social sciences. It will enable the students to know what is statistics, how and when to apply statistical techniques to decision making situations and how to interpret the results. Class Room Policies: 1. Student will be allowed to enter the class till the attendance is going on, after that no one can enter the class. 2. No student will be given a chance to reappear for MSE. 3. All the tests will be considered for internals. 4. Each assignment will have weightage & assignments are to be submitted by the scheduled time, failing which no assignment will be accepted. Internal Marks Distribution: Mid Semester Examination: 15 Presentation: 6 1st Hourly Tests: 5 2nd Hourly Tests: 5 Class test: 5 Assignment: 4
- 3. Lecture No. Contents Assignments 1. Introduction to Business Statistics • Relevance • Applications 2. Functions of statistics • Definiteness • Condensation • Comparison • Prediction • Formulation Of suitable policies Limitations • True only on average • It can be misused • One method of studying the problem • Does not deal with individual measurements 3. Data • Relevance • Collection of Data 4. Classification of data 5. Collection of chocolate preference (Activity-1) 6. Formation of discrete Continuous frequency distribution 7. Tabulation of data • meaning • Relevance • Format of table 8. Case study -1(Portfolio management) 9. Graphic presentation: Meaning Types of diagrams • Sub-divided bar • Multiple bars • Percentage bar • Pie Chart 10. Graphic presentation (contd.). • Graphs of frequency distribution • Frequency Polygon • Frequency curve • Ogives 11. Practical Tutorial- 1 Discussion on the problem of students. 12. Measures of central value / Measures of Location Assignment-1 Relevance Objectives of averaging Requisites of a good average 13. Arithmetic mean # Calculation in Individual 14. Calculation of mean in descrete and continuous series 15. Geometric mean 16. Harmonic mean 17. Median
- 4. REFERNCES 1. Levin & Rubin: Statistics for Management, Prentice Hall India. 2. Srivastava & Rego : Statistics for Management, Tata McGraw Hill 3. S.P.Gupta : Statistical Methods, Sultan Chand & Sons 4. Andersons, Sweeny and Williams : Cengage Learning, Statistics for Business and Economics Activity-1 Students will go to 25 children and ask them about their chocolates’ preferences among the various brands available in the market. They will collect the data about the name and age of the children along with their preferences. Then, they will convert this raw data into a Bivariate Table consisting of 2 variables. 1. Chocolate 2. Age For Example: X(Chocolate)/Y(Age 3-5 5-7 7-9 9-11 11-13 13-15 ) Dairy Milk sMilky Bar Munch Perk
- 5. Nestle 5 Star Bar One Activity-2 Calculate the relationship between the marks obtained in 10th & +2 of 15 students. Assignment-1 Draw the Histogram, Frequency Polygon and Frequency Curve: 1. Variable Frequency Variable Frequency 100-110 11 140-150 33 110-120 28 150-160 20 120-130 36 160-170 8 130-140 49 2. Salary (p.m.) No. of employees Less than 3000 100 3000-4000 20 4000-5000 30 5000-6000 60 6000-7000 75 7000 & More 115 Assignment-2 1. Calculate Median & Mode of the data given below. Using them find arithmetic mean. Marks 10 20 30 40 50 60 Less Than No. of 8 23 45 65 75 80 students 2. Find the class intervals if arithmetic mean of the following distribution is 33 & assumed mean 35. Step -3 -2 -1 0 1 2 Deviation
- 6. Frequency 5 10 25 30 20 10 Assignment-3 1. Calculate Karl Pearson’s Coefficient Of Correlation from the following data: X 100 200 300 400 500 600 700 Y 30 50 60 80 100 110 130 2. Find Rank Correlation X 50 55 65 50 55 60 50 65 70 75 Y 110 110 115 125 140 115 130 120 115 160 Presentation Topics Every group will take up any Organization according to their convenience and will collect the data relating to its sales and Production (month wise for 4 years) and will show the same for every year in graphs and will have to find the average sales and production during the year and the combined mean for all the 4 years. The students will be divided into the group of 3. Each group will have to present within 20 minutes. Presentation Assessment Break Up Presentation Report 3 Communication skills 4 Formals 1 Query handling 2 Formulae Of Statistics In Course Arithmetic mean Direct Method In Individual Series A.M.= ΣX/N In Discrete & Continuous series A.M.= ΣFX/ΣF
- 7. Short Cut Method/ Indirect Method A.M.= A+ΣFdx/ΣF Step-deviation Method A.M.=A+ΣFdx'/ΣF*i Geometric Mean G.M.=√ab Harmonic Mean In Individual Series N/Σ(1/X) In Discrete & Continuous series N/Σ(f*1/X) Median In Individual & Discrete Series M=N+1/2, (Nth term+N+1/2)/2 Continuous series N1=N/2, M=L+ N1-CF/F*i Mode In Individual Series Maximum repeated term In Discrete & Continuous series Groupung Table & Analysis Table, M= L+D1/(D1+D2)*i Quartiles In Individual & Discrete Series Q1=N+1/4, Q2=2(N+1)/4, Q3=3(N+1)/4 Continuous series N1=N/4, Q1=L+(N1- C.F.)/F*i,N1=3N/4,Q3=L+(N1-C.F.)/F*i Decile N1=N/10, D1=L+(N1- C.F.)/F*i,N1=9N/10,D9=L+(N1-C.F.)/F*i Percentile N1=10(N/100), P10=L+(N1- C.F.)/F*i,N1=90N/100,P90=L+(N1-C.F.)/ F*i Measures of dispersion Range Highest Value-Lowest Value Quartile Deviation Q3-Q1/2 Coeffcient of quartile deviation Q3-Q1/Q3+Q1 Mean Deviation In Individual Series Σ[X-A.M.]/N In Discrete & Continuous series ΣF[X-A.M.]/N Coefficient Of Mean Deviation M.D./A.M.or M or Z Standard Deviation In Individual Series √Σd²/N-(Σd/N)2 In Discrete & Continuous series √Σfd²/N-(Σfd/N)2 Coefficient Of Standard Deviation S.D./A.M. Variance S.D.² Coefficient of variation S.D./A.M.*100 Coefficient Of Correlation Karl Pearson r=NΣXY-(ΣX.ΣY)/√(NΣX²- {ΣX}²).√(NΣY²-{ΣY}²)
- 8. Spearman 1-6ΣD²/N³-N When ranks are not repeated 1-6[ΣD²+1/12{m³-m}]/N³-N, When ranks are repeated Concurrent deviation C √n (2C-n/n) Standard Error 1-r²/√N Probable Error 0.6745 (1-r²/√N)