Get the Complete Business Statistics Notes from Glad Tutor. No matter whether you are a B.COM 2nd year, BBA 2nd year or MBA student, we have designed our notes keeping all in mind. These are the handmade lecture notes prepared according to the syllabus of the popular business management colleges and universities. Our Business Statistics Notes includes both theory and also practical questions.

## Topics covered in Business Statistics Notes

The Topics of Business Statistics Notes are as follows-

**Unit-1:**

- Probability Theory- Basic Concepts and Approaches, Rules or Theorems-Addition Rule, Multiplication Rule, Complement Rule, Conditional Probability, Bayes Theorem.
- Probability Distribution- Meaning, Characteristics, Classification of Variables.
- Bernoulli Distribution- Meaning, Formulas with the illustration.
- Binomial Distribution- Meaning, Conditions, Properties, Formulas, 2-3 Illustrations.
- Poisson Distribution- Meaning, Formulas, 2 illustrations, Properties.
- Continuous Probability Distribution- Normal Distribution Properties, Formulas, 3 Illustrations.

**Unit-2**

- Sampling: Need, Significance and Methods of Sampling- Probability and Non-Probability Sampling.
- Errors of Sampling-Sampling and Non-Sampling Errors.
- Law of Large Numbers, Central Limit Theorem, Large and Small Sampling Distributions.

**Unit-3**

- Statistical Estimation: Estimates, Estimators, Properties of Good Estimator.
- Point and Control Estimations of Population Mean, Proportion and Variance
- Statistical Testing: Hypothesis, Law of Significance, Steps in Hypothesis Testing and Errors.
- Large and Small Sample Tests- z-test, t-test and f-test with Illustrations.

**Unit-4**

- Non-Parametric Tests: Chi-Square Tests of Goodness of Fit, Independence and Homogeneity.
- Test of Equality of several Population Proportion, Sign Test, Wilcoxon Signed-Rank Test, Wald-Wolfowitz Test, Kruskal Wallis H Test.

**Unit-5**

- Role of Statistics in Quality Management: Significance and Introduction.
- Statistical Quality Control: Quality Control Charts for Variables and Attributes
- Acceptance Sampling

## Introduction to Business Statistics Lecture Notes

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The topic includes the Probability- its Meaning, concepts and approaches, Rules or Theorems- Addition Role, Multiplication Rule, Complement Rule, conditional probability and Bayes Theorem.

## Meaning of Probability

Probability is the numerical or quantitative measure of uncertainty. It shows the strength of your beliefs in the happening of an uncertain event. It mainly lies between 0 and 1. It is very useful in making future decisions.

### Basic Concepts of Probability

There are basically three concepts of Probability that are as follows-

**Experiment-**An Experiment is any type of process that leads to one or more than one possibilities. It further categorises into two more parts- Random Experiment and Deterministic Experiment. Random Experiment is a process which has one or more than one outcomes. Deterministic Experiment is a process which has only one outcome.**For Example-**Tossing a Coin, throwing the dice.

**Sample Space-**Sample Space of an experiment is the universal set of all the possible outcomes of an experiment. It is represented by n(s).**For Example-**The Sample Space of the Tossing a Coin will be n(s)= {H, T}

**Event-**Event is the subset of the sample space in which we are interested in the happening or non-happening of a certain event. It is denoted by n(a).**For Example-**If You are interested in knowing the Probability of getting the Heads. The Event will be- n(a) = {H}

**Illustration- **What is the probability of getting one Head when we toss two coins?

**Sol- ** n(s)= {HH, TT, HT, TH} = 4

n(a)= {HT, TH} = 2

P(a) = n(a)/n(s)

= 2/4

=0.5

### Approaches to the Definition of Probability

**Classical Approach-**It is a type of approach which is all equally likely or universally applicable. In this, there is no requirement of personal judgement.**For Example-**Everyone knows tossing a coin can result in only two possible outcomes- Head or Tail which everyone knows.

**Relative Frequency Approach-**It is a type of approach in which either it is not possible to achieve the outcome or to achieve in which past data is available.

**Subjective Approach-**It is a type of approach which requires personal judgement.**For Example-**Doctor assigning the Patient for its disease which requires their personal judgement.

### Rules or Theorems of Probability

The Rules or Theorems of Probability are of six types that are as follows-

**Addition Rule-**This rule allows you to know the probability of the union of two or more events in terms of individual probability and probability of their simultaneous occurrence.

For Two Events, the Addition Rule will be p(AUB)= p(A) + p(B) – p(A∩B)

For More than Two Events, it will be p(AUBUC)= p(A) + p(B) + p(C) – p(A∩B) – p(B∩C) – p(A∩C) + p(A∩B∩C)

It can be better explained with the help of one Example.

**Illustration- **A Card drew from a pack of cards. What is the probability that it is either a Black Card or King or Club?

**Sol- **Let A, B and C be the events for the cards drawn for Black Card, King and club respectively.

P(A)= 26/52 P(B)= 4/52 P(C)= 13/52 P(A∩B)= 2/52 P(B∩C)=1/52 P(A∩C)=13/52 P(A∩B∩C)=1/52

P(AUBUC)= P(A)+P(B)+P(C)-P(A∩B)-P(B∩C)-P(A∩C)+P(A∩B∩C)

= 26/52+4/52+13/52-2/52-1/52-13/52+1/52

= 44/52-16/52

= 28/52

**Multiplication Rule-**Multiplication rule is the rule which helps us to find out the probability of two occurrences simultaneously. In Multiplication rule of Probability, there is a different formula for Dependent and Independent Events.

For Dependent Events | For Independent Events, |

P(A∩B)= P(A/B)P(B)P(B∩A)= P(B/A)P(A) | P(A∩B)= P(A).P(B) |

**Illustration- **A Box contains 10 balls from which 2 are green, 5 are red and 3 are black. Two Balls drew at random one after the another. Find the probability that both the balls are of green colour.

(i) with replacement (ii) without replacement.

**Sol. (i)** Let G1 and G2 are the events for getting the two green balls respectively.

P(G1∩G2)= P(G1).P(G2)

= 2/10.2/10

= 4/100= 0.04

**(ii)** P(G1∩G2)= P(G1/G2).P(G2)

=1/9.2/10

=2/90

=1/45

**Complement Rule-**It is the part of the sequence space in which it is not included.**For Example-**To Find out the Complement of A, it will be-

** **P(A`)= 1-P(A)

**Conditional Rule-**Conditional Rule is the rule in which the happening of one event has a relation or no relation with the happening or unhappening of another event. The formula of the conditional rule-

P(A/B)= P(A∩B)/P(B)

**Law of Total Probability-**This rule is mutually exclusive and collectively exhaustive.

n(A)/n(S)= n(A∩B)/n(S)+n(A∩Bc)/n(S)

P(A)= P(A∩B)+P(A∩Bc)

**Illustration- **A Market Analyst believes that the Stock Market has the 0.70 probability of going up in the next year if the economic conditions too well and 0.20 probability of going up if economic conditions don’t go well. The Analyst believes that there is 0.80 probability that the economy will do well in the coming year. What is the probability that the economy will go up next year?

**Solution- **Let U be the event that the stock market will be up in the next year and W be the event that the stock market will do well in the coming year.

P(W)= 0.80 P(W`)=0.20 P(U/W)=0.70 P(U/W`)=0.20

P(U) = P(U∩W) + P(U∩W`)

=P(U/W).P(W)+ P(U/W`).P(W`)

=(0.7)(0.8)+ (0.2) (0.2)

=0.56+ 0.04

=0.60

**Bayes Theorem-**This Theorem is helpful in revising the additional information.

P(B1/A) = P(A∩B1)/P(A)

P(B1/A)=P(A/B1).P(B1) / P(A∩B1) + P(A∩B2)

(Using the Multiplication Formula of P(A∩B1) and Law of Total Probability Formula of P(A).

P(B1/A) = P(A/B1).P(B1)/ P(A/B1).P(B1)+ P(A/B2).P(B2)

**Illustration- **In a Class of 50 Students, 30 students refer to a book by Author A and 20 Students refer to a book by Author B. 3% of the students who refer Book A and 1% of the students who refer to Book B by the advice of their teachers. A Student has randomly selected and found that he is using a book recommended by his teacher. What is the probability that he is using a book recommended by Author A?

**Solution- **Let B1 and B2 are the events for the students who refer to book author A and B respectively.

Let X be the event for the students who refer to books with the advice of their teachers.

P(B1)=30 P(B2)=20 P(X/B1)=0.03 P(X/B2)=0.01

P(B1/X)= P(X/B1). P(B1)/ P(X/B1).P(B1)+ P(X/B2).P(B2)

= 0.03(30)/(0.03)(30)+(0.01)(20)

= 9/9+2

=9/11

=0.81

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