Category: Commerce Notes PPT

Mean, Median and Mode are the three statistical measures often used to encapsulate data sets. They are mainly known by the expected name “average”. There are many “averages” in statistics, but these three are the most common. 

The “mean” is mainly the “average” where all the numbers are added up and then divided by the number of digits. The “median” is the “middle” value in the number series, and the “mode” is the value that occurs on numerous occasions. Out of these three measures, the mode formula in statistics opens different ranges and aspects for the student’s

Formulas of Mean and Median

The first theory to understand from the mean, median, and mode is mean. As described above, the mean is the ratio of summation of all the values to the number of items. There are two types of Mean – simple arithmetic mean, and weighted arithmetic mean. If you want to know what is the formula of mean, go through the section given below:

[ Mean= frac{sum X}{ N}]

Here, [ sum X]= Sum of individual values and =Total number of Items

The simple arithmetic mean examine values in data as equal and permits equal importance to each value. On the other hand, in weighted arithmetic mean, weights or importance is assigned to the values.

To find the Median, the numbers should be arranged in numerical order from smallest to highest. Taking the number of observations as (n), and “th” signifies the (n)th number –

Median Formula = [frac{(n+1)}{2} th]

Students who are looking for mean, median, mode formula pdf can wish to visit the official website of . 

Mode Formula in Statistics for Discrete Series: 

Mode comes third in the concept of mean, median, and mode. As discussed earlier, it merely refers to the value that occurs most frequently in a number series. In discrete series, the values of items with their equivalent frequencies are found. Essentially, the value of the items with the highest frequency will be the mode for the distribution. Mode formulae in statistics help the students to solve different complicated statistical problems in their textbooks. Students can follow this method of mode in discrete series from an example shown below –

Example 1 – Find Mode from the following data

Ans: Arranging data in ascending order

The term that is occurring the maximum number of times is considered as Mode (Z). Here we get 16 four times, 12 and 20 two times each, and other terms once only. Thus Z=16

Students can find more examples of mode calculation in discrete series in ’s online classes.

Illustrating Measures of Central Tendency

Mean, median, and mode are together known as measures of central tendency. It signifies a synopsis of data that represents the center point or quintessential value of a dataset. These measures specify where most values in a distribution fall and are also referred to as the central location of a distribution. Best measures of central tendency can be chosen depending on the data you have. A “measure of central tendency” is either a location framework or a statistic used to evaluate a location parameter.

Several Measures of Central Tendency

• Arithmetic mean

• Median

• Mode

• Geometric mean 

• Harmonic mean

• Generalized mean

• Weighted mean

• Truncated mean

• Interquartile mean

• Midrange

Students can solve their statistical problems with measures of central tendency formulas that are given below –

Arithmetic Mean [ (overline{X} = frac{sum X}{N})]

(Where [sum X] is the summation of all the observations provided in a dataset and “n” is the number of observations)

Median formula= [ frac{{(n+1)}}{2}]

Mode Calculation for Continuous Series

While demonstrating the mode formula for continuous series, it is only one step forward of the method for discrete series. We get the value of Mode by interposing as in the case with a median. Mode formula in statistics is easy to understand and pretty simple to calculate Formula provided below has been used to calculate Mode (Z):

Mode (Z) = [L + frac{f_{1} – f_{0}}{2f_{1} – f_{0} – f_{2}} * i]

Where L= lower limit of modal interval

[f_{1}]= frequency correlating to modal interval

[f_{0}]= frequency heading modal interval

[f_{2}]= frequency succeeding modal interval

[i]= length of modal interval

Several Points While Calculating Mode –

• Class intervals must be absolute

• Length of the classes should be equal

• Series should be arranged in ascending order

• If the series is increasing, then convert it into continuous series

• If the first class is considered as a modal class, then f0 will be zero

• Similarly, if the last class is considered as a modal class, then f2  is zero

Students can have access to online resources where they can get innumerable solutions considering the formula of mode in continuous series. To know more about this topic, download ’s app now!

The mean, median, and mode are the three classifications of central tendency.           

Mean

The arithmetic average of the given data set which is found by the division of the data set by the total number of observations in the data set is referred to as the mean of the data set.

[ overline{x} = frac{sum x}{N}]

where the summation is represented by [ sum]

observations are represented by x

number of observations is represented by N

If the data is presented in a tabular form, in this case, the formula used to compute the mean is

Mean=[ frac{sum f x}{sum f} ]

Where [ sum f = N]

Median

The middle number in the data set is referred to as the median when the numbers are listed in either ascending or descending order.

In the case when the total number of observations (n) is an odd number, then the formula of the median is given by-

[Median = left ( frac{n+1}{2} right )^{th}observation]

In the case when the total number of observations (n) is an even number, then the formula for the median is given by-

[ Median = frac{(frac{n}{2})^{th}observation + (frac{n}{2} + 1)^{th} observation}{2} ]

When the data is continuous and is presented in form of the frequency distribution, then the median given by-

[Median=1 + left [ frac{(frac{n}{2}) – c}{f} right ] times h]

where the lesser limit which belongs to the median class= l

cumulative frequency value before the median class= c

frequency that is possessed by the median class= f

size of the class= h

Mode

The value in a data set that has occurred the most number times is referred to as the mode and the difference between the highest and lowest values of the data set is referred to as the range.

To calculate mode in a data set, the following steps are followed-

1. Determination of the modal class that possesses the maximum frequency.

2. Calculation of the mode by the formula- [Mode= 1+ left [ frac{f_{m}-f_{1}}{2fm-f_{1}-f_{2}} right ] times h]

where frequency possessed by modal class= [f_{m}]

frequency possessed by the class that is before the modal class= [f_{1}]

frequency possessed by the class that is after the modal class= [f_{2}] 

Lesser limit of modal class= l

Width of the class= h

A circular, a letter or a notice are very important communication tools in a business organization. The importance of these communication tools cannot be underestimated as they enable you to disseminate critical information to the people, so as to provide relevant and latest information regarding the business. You can also use these tools to invite the potential consumers, clients, suppliers, and partners for any upcoming events or conferences. Apart from this, circulars also make for a great marketing tool to reach the target audience.

In this context, we will understand about Circulars, the structure of circulars and its advantages will be discussed as well. 

Circulars – a Crucial in Official Communication

Irrespective of the size, work, duties, and services of any organization, communication is one of the most crucial aspects of its working. Official communication plays a vital role in the efficient and smooth working of an organization. Effective communication between employees, authorities, departments, and clients takes the organization ahead on the path of success. Circular is the most important tool of official communication. In this section, we shall study in detail the concept of circulars, their purpose, and their importance for communication on an official platform. In this part, we will learn about circular writing and its importance, in detail. 

What is a Circular?

A circular is the official communication medium which a business organization communicates. As the name itself tells, it is a letter which is given to the audience. Circulars have four components: head, opening, text, and signature. If you receive a circular from an organization or its team of employees, then it means that the organization is planning to inform you about something. The term circular comes from the fact that it was written on a circular piece of paper. Although circulars can be written on any kind of paper, the most frequently used type is the “letterhead”. Circulars are generally used in the context of businesses and public service organizations.

In a general sense, a circular is a statement about a business or about a company which is issued by the firm. A circular can be addressed to customers, suppliers, customers, employees or to any other business group. These documents are used for many different purposes in the context of businesses. 

The Structure of a Circular

As a circular is a letter, it must have a heading and a body, which contains the required information about the sender. The head will include the information about the recipient, addressee or readers and it is considered the important part of the circular. The opening is a section where the sender introduces himself or herself. In this section, the sender provides the information about his business, his name, the title, etc.

The body will contain information regarding the purpose, content or information conveyed by the circular, so it must be relevant to the recipients. The closing is used for ending the letter or for the sender’s signature. 

The use of circulars in organizations is very common because they are direct and to the point. In circulars, organizations want to inform their customers about the company, about the services offered or to explain the new developments within the organization. They might notify you about the business, the goods that are being sold, a new promotion or a new product release. Circulars can also be written to employees to inform them about the plans of the organization or they can be written to the partners or suppliers for the purposes of advertising.

In the corporate world, different heads may be present in a circular. The most important one is the head that is present at the beginning of the letter. In this head, the sender will be introduced and will mention his/her title or name. After that, a brief introduction will be presented. 

The name of the organization may be mentioned, followed by the location and the format of the letter, like business letter format. Also, it can be written that the letter is circular. This is the official form of the letter and if it is written correctly, it might be easily spotted. Other important heads are the subject head and the closing.

An example of a company circular has different styles of writing, but it is mainly written in a formal tone. A company circular is written in a professional manner to give the impression of reliability. They should also follow a certain writing format to avoid any doubts. The subjects of the company circular are usually a few sentences or a paragraph. This is because the company does not have to write a lengthy letter for them.

In order to make the corporate circular more personalized, the company can choose to use some different fonts. Apart from the formal fonts, they might also choose an informal font that can make them more readable to the recipients. They can even use different sizes of the fonts if they want to.

The content of a company circular should be concise and should include all the details that should be included in the letter. In short, it is not a good idea to include lots of information in the letter. Also, the letter should have a professional presentation. It is better if it has the signature of the person who wrote it. This will help to add credibility to the letter. A good way to do it is to print the company name and then sign the letter.

Circulars in Professional Sector 

In the professional sector, there are few instructions, updates, and information that is to be circulated amongst a large number of people. In such cases, circulars are extremely helpful. Circular is an essential letter containing important information that is to be circulated to a large section of people. In Business Communication, circular plays a vital role in the smooth functioning of any organization. 

For example, there is some important information that you need to discuss with your employees. For this purpose, you will have to set up a meeting with your employees. The meeting can be held only when you convey the exact timings, place, and purpose of meeting to your employees in the minimum time. In such situations, spreading the message through circulars can be the most efficient and time-saving mode of communication. 

You can always add marketing information in circulars and use them for mass distribution. The main and most vital feature of circulars is that it conveys information to a large number of correspondents in the minimum time.

Advantages of Circulars

Circulars, if designed and distributed productively, play an important role in the growth and development of business. It is some of the vital letters used in corporate sectors, schools, colleges, and various workplaces to convey important updates. The advantages of circulars are discussed below briefly.

It is a straightforward and most convenient method of conveying important information to a large group of people. Circulars play an important role in the growth, development, and smooth working of any business. The information can be conveyed at a greater level at cheap rates. It is also useful in producing prompt feedback from the respondents. 

In broader terms, circulars can also be used for wide publicity. To convey the news related to product, service, or customers, circulars are used as they help to expand the business and market base of a company. As a result, the large amount of money that would have been used in sending separate letters can be saved. 

With the efficient use of circulars, any important information can be transmitted to a large section of people at the same time. Hence, it saves you a lot of time that the company officials might spend on conveying the information separately to different people. Circulars can be displayed on the notice board of the workplace, and people can read the relevant information. This time-saving method becomes very convenient for companies.

Circulars are a cost-effective method of spreading information. Since with the help of just one circular information can be given to a hundred people. It thereby reduces the printing cost as well as the distribution cost of information per reader. With this method of passing information, an organization can save a lot of money for better purposes. 

Circulating information separately to all the concerned individuals requires a lot of work and effort. It becomes both time-consuming and difficult. With the use of circular letters, an organization can effectively overcome this problem with an efficient solution. Circular letters help to communicate with a large number of people with minimum effort. 

Rightly designed, convincing, and attractive circular letters can easily convince a reader about the importance and benefits of the data mentioned in the circular. It thereby enhances a consumer’s trust and confidence in the company’s products. 

One must design the circulars very carefully. If the correct information about the price, utility, and place of availability of the product is mentioned in the circular letter, the general public reading that particular circular becomes more conscious about the product. These letters also help to inform the customers about social welfare activities, quality of the product, and services, thus engaging them more with the company.

A well-designed circular letter can win the hearts of hundreds of customers at a time. It contributes a lot of positive aspects to the reviews, services, and awareness of the company by enhancing the goodwill of the company on a mass level. 

Conclusion

A company circular is a letter that is addressed to the shareholders of the company. Its primary objective is to inform them about the progress that the company has made during a period of time. It should be written in a professional manner that makes it easy for them to read and understand. The main goal of a company circular is to inform the shareholders about the progress of the company. They should be in a concise and a well-written letter that includes all the relevant details.

In our daily lives, we may encounter many forms of contract such as an insurance policy, lease agreements, employment contract, non-disclosure agreement etc. Even a marriage license is a type of legally binding contract. Hence, one should have a comprehensive knowledge of all the essential aspects of a contract. It can be defined as a written or oral agreement between two or more parties that is enforceable under law. 

 

Furthermore, all the parties involved should be mentally sound and agree to enter the contract voluntarily. An agreement has three main components – offer, acceptance, and consideration. Additionally, one should also know about the communication of offer and acceptance.

 

Consideration

Consideration is an act of value that one of the parties provides to another in exchange for successful fulfillment of the terms and conditions of the contract. Without it, an agreement is null and void. However, consideration needs to satisfy some parameters to be considered valid – it should not involve illegal or fraudulent activities, such as causing damage to a person or property. Moreover, it should be offered at the desire of the promisor. It can also come from a third party. 

 

Offer

Before a contract is drawn up, an offer is placed by one party to another. An offer is a promise to perform or abstain from an act at the desire of the other party in exchange for consideration. It should also contain a statement that communicates intent to enter into a contract. 

 

The party that makes an offer is known as the offeror, and the individual who accepts it is known as an offeree. For instance, if A offered to paint B’s house for a sum of money, then A is the offeror and B is the offeree. An offer can be categorized into two types – unilateral and bilateral. 

• Unilateral – It is a type of offer that is made to the general public at large. This type of offer includes only the promisor who makes an open offer which anybody can enter into. For instance, advertisements can be considered unilateral offers. Display of goods by a vendor can also be a unilateral offer as any individual can choose to buy a product or service from a shopkeeper which results in a contract.  In this case, the offeror does not wait for communication of acceptance.

• Bilateral – An offer that is made to a specific individual or a group of individuals is called bilateral. In this type of offer, acceptance must be communicated, and all parties involved promise to provide some consideration to others.

 

Communication of Offer Acceptance and Revocation

An offer can only be considered valid after it is communicated to the offeree. Communication of offer in contract law is only complete when it is conveyed to the other party and is accepted by them. The offer can be dispatched through any common means such as post, email, telephone or through word of mouth.

 

Additionally, communication of acceptance of an offer is also necessary since an offer only becomes a contract after the individual to whom it was sent gives his or her consent to it.  Some conditions need to be met while accepting a proposal which has been given below – 

• Acceptance must be communicated to the offeror through written or oral means as silence will not be considered a valid form of approval.

• The communication of acceptance of an offer should be absolute. 

• The offer will be considered accepted, once the promisee dispatches their acceptance. 

• In case of instantaneous communication in contract law cases, such as telephone, email, fax, a contract will form only when the offeror receives the offeree’s acceptance. It is not so in the case of postal communication. 

• It is also vital that the communication of acceptance is carried out either by the offeree or an authorized agent hired by him or her.  If any other individual dispatches the approval, it is not considered valid. 

 

An example of communication of acceptance cases is the Powell vs Lee case; Powell applied for the post of headmaster which was accepted by members of the school board.  Plaintiff heard through a person who was on the board that he had been appointed for the post. 

 

However, he later came to know that he was not selected and he sued the school board for breach of contract. The court ruled that since the communication of acceptance was not relayed by an authorized agent, there was no breach of contract. 

 

Communication and Revocation of Offer and Acceptance

Revocation of the offer refers to when an offer has been terminated or canceled.  A proposal can be revoked by the offeror at any time before the communication of acceptance is dispatched by the offeree but not afterwards. On the other hand, the offeree may revoke his acceptance any time before the post conveying it reaches the offeror but not later than that.

A revocation of a proposal may take place in the following instances – 

• When the offeror passes away or gets diagnosed as mentally incompetent, and the offeree comes to know the fact before the communication of acceptance of a proposal.

• When the offeror notifies the other party regarding the Revocation of the offer

• After the time specified by the offeror has passed. Additionally, in situations where no time has been stipulated, then the offer can be rejected after a reasonable amount of time has been mentioned.

• The offeror can reject the proposal if the other party fails to fulfill a necessary condition

When we purchase various products we tend to check the manufacturing date and company, expiry date or year of the expiry of the warranty, check the nutritional count if it is a food product and so on. We perform a thorough quality check and go through the terms and conditions before purchasing any product. Especially if we purchase electronic goods like a laptop we are more careful than ever in checking for its specs, manufacturer and seller, the quality of the piece and the year until when its warranty is valid. 

When we go for intangible services too, we tend to check the reliability of a service provider and quality of services offered before making a decision, be it checking into a 5-star hotel, booking vacation packages or installing WiFi at home. 

A sales agreement happens when a buyer and a seller thus engage in a material transaction. Warranty and conditions are two important components of this transaction. 

What are a Condition and Warranty?

Conditions can be defined as certain obligations, terms or provisions that are associated with the transaction between a buyer and seller. Breach of these conditions can lead to cancellation of agreement and violation of warranty. The non-offending party can also claim appropriate reimbursements and cancel the existing contract as well. A warranty can be expressed or implied. 

What are the Types of Conditions?

Implied conditions are those terms that are not explicitly stated but rather understood and legalised as per the law – 

1. Implied Understanding Regarding Title – Here, it is implied that the seller can sell his goods with all rights and transfer ownership to the buyer. It is understood that before the transaction takes place, the seller is the owner of the goods. In case of any defects, the buyer can claim damages as per the conditions and warranty. It is implied that no fraudulent third party charges will be imposed upon the goods. 

2. Implied Knowledge of Quality and Fitness – The buyer engages in a transaction with the seller with the belief that about the seller’s skill, that he can sell appropriate goods and the seller is aware of the intentions of the buyer.

3. Sale by Description – If the goods are being sold as per the description of the product, then the warranty and conditions will be in accordance with the same. If there is a sample involved as well, then the warranty and conditions will again conform to both. 

4. Sale by Sample – When products are being sold as per the samples earlier marketed, it is implied that the warranty and conditions for the bulk products have to match the quality of the original sample. Buyers should receive sufficient time to compare what they purchase with the quality of the sample and check for defects if any. 

5. Expressed Conditions – The terms and conditions that are explicitly stated in the sale agreement are known as express conditions. Buyers should go through this and have a complete understanding before purchasing.

Consumer organizations are the focused group that seek to protect people from the corporate abuse led by the business owners – like unsafe products, predatory lending, false advertising and pollution to the environment. Consumer Organizations may even operate through the protests.

Today, consumer organisations are playing a dominating role in engaging the consumers to lift their voice against exploitation by the business individual who sells inferior and faulty products. In educational institutions also consumer rights are taught, to prepare the student’s courses of study by keeping in view the interests of the consumers in the society. In our discussion, we are going to know about the consumer protection forums that operate in India.

Consumer Organizations

In the capitalistic system of the Market or economy privatization is the basic mode of production. And consumers remain as individuals responsible for their choice of products. With the growing times, these manufacturing companies become big organized houses having a considerable command over all the products available in the market. Unlike entities controlled by the democratic or other forms of government the motive of such private enterprises is only to make a profit. So there have been instances of manipulation and adulteration of products as an insincere way of earning money. Or sometimes they indulge in the methods of dissemination of misinformation to a consumer and exploit them for their hard-earned money. This is more common in scenarios where products are services provided by any privately-owned companies. In such settings, victims often find themselves helpless against such business entities for the reclamation of their lost money or remediation of their misery. By the late 19th century various movements started to emerge for the protection of consumers from giant corporate houses. These movements translate into Consumer Organizations all over the world. Such groups were meant to be the voice of general consumers getting abused of any kind. They often take the course of litigation, protest, campaign or other means of peaceful actions. 

In India, there are also many Consumer Organizations working for the cause of customers getting abused by manufacturers or service providers. To give an illustration the names of organizations are Akhil Bhartiya Grahak Panchayat, Consumer Guidance Society of India, All India Consumer Protection Organization, The Consumers Eye India, United India Consumer’s Association, Grahak Shakti, Coordinated Action of Consumer & Voluntary Organizations, Consortium of South India Consumer Organizations (COSICO), Consumer Awareness, Protection and Education Council (Cape Council), Consortium of South India Consumer Organizations (COSICO). The Ministry of Consumer Affairs, Government of India, has also started a consumer awareness program called ‘Jago Grahak Jago’.

These Non-governmental Organizations are also always active by collecting data and survey reports of the product tests and for the user experience of various products and services. The information gathered helps them to find any corrupt practices in the market and generate awareness about the same.