Category: Commerce Notes PPT

To simply understand what National Income is, it can be represented as – National Income defines a country’s wealth. This income depicts the value of goods and services which are produced by an economy. This gives effect to the net result of all the economic activities performed in the country.

Imagine how you would define a country’s wealth without any economic term? In that case, there would be no accountability and responsibility linked with the production in the country. The resources would go uncalculated and there would be a vague economic atmosphere. Thus, let us indulge in this study which talks about National Income. 

Understanding National Income

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National income is the sum total of the value of all the goods and services manufactured by the residents of the country, in a year., within its domestic boundaries or outside. It is the net amount of income of the citizens by production in a year. 

To be more precise, national income is the accumulated money value of all final goods and services produced in a country during one financial year. Computation of National Income is very vital as it indicates the overall health of our economy for that particular year.

The aggregate economic performance of a nation is calculated with the help of National income data. The basic purpose of national income is to throw light on aggregate output and income and provide a basis for the government to formulate its policy, programs, to maximize the national welfare of the people. Central Statistical Organization calculates the national income in India.

Definition of National Income

The definition of National Income if of two types-

Traditional Definition of National Income-

According to Marshall: “The labor and capital of a country acting on its natural resources produce annually a certain net aggregate of commodities, material and immaterial including services of all kinds. This is the true net annual income or revenue of the country or national dividend.”

Modern Definition 

This definition has two subparts

Gross Domestic Product

Gross Domestic Product, abbreviated as GDP, is the aggregate value of goods and services produced in a country. GDP is calculated over regular time intervals, such as a quarter or a year. GDP as an economic indicator is used worldwide to measure the growth of countries economy.

 

Goods are valued at their market prices, so:

• All goods measured in the same units (e.g., dollars in the U.S.)

• Things without exact market value are excluded.

Constituents of GDP

• Wages and salaries

• Rent

• Interest

• Undistributed profits

• Mixed-income

• Direct taxes

• Dividend

• Depreciation

The Formula for Calculation of GDP

GDP = consumption + investment + government spending + exports – imports.

Gross National Product

Gross National Product (GNP) is an estimated value of all goods and services produced by a country’s residents and businesses. GNP does not include the services used to produce manufactured goods because its value is included in the price of the finished product. It also includes net income arising in a country from abroad.

Components of GNP

• Consumer goods and services

• Gross private domestic income

• Goods produced or services rendered

• Income arising from abroad.

Formula to Calculate GNP

GNP = GDP + NR (Net income from assets abroad or Net Income Receipts) – NP (Net payment outflow to foreign assets).

Importance of  National Income

Setting Economic Policy

National Income indicates the status of the economy and can give a clear picture of the country’s economic growth. National Income statistics can help economists in formulating economic policies for economic development.

Inflation and Deflationary Gaps

For timely anti-inflationary and deflationary policies, we need aggregate data of national income. If expenditure increases from the total output, it shows inflammatory gaps and vice versa.

Budget Preparation

The budget of the country is highly dependent on the net national income and its concepts. The Government formulates the yearly budget with the help of national income statistics in order to avoid any cynical policies.

Standard of Living

National income data assists the government in comparing the standard of living amongst countries and people living in the same country at different times.

Defense and Development

National income estimates help us to bifurcate the national product between defense and development purposes of the country. From such figures, we can easily know, how much can be set aside for the defense budget.

Sets of methods for measuring National Income

There are four methods of measuring national income. The type of method to be used depends on the availability of data in a country and the purpose which is attempted for.

Income Method

In this method, we add net income payments received by all citizens of a country in a particular year. Net incomes that result in all the factors of production like net rents, wages, interest, and profits are all added together, but income received in the form of transfer payments are omitted.

Product Method

According to this method, the aggregate value of final goods and services produced in a country during a financial year is computed at market prices. To find out GNP, the data of all the productive activities-agricultural products, Minerals, Industrial products, the contributions to production made by transport, insurance, communication, lawyers, doctors, teachers. Etc are accumulated and assessed.

Expenditure Method

The total expenditure by the society in a financial year is summed up together and includes personal consumption expenditure, net domestic investment, government expenditure on goods and services, and net foreign investment. This concept is backed by the assumption that national income is equal to national expenditure.

Value Added Method

The distinction between the value of material outputs and material inputs at every stage of production is Value added.

GDP Vs GNP

The Gross Domestic Product and the Gross National Product are the two most widely used measures in a country’s calculation of aggregate economic unit.

GDP is the measure of the value of goods and services that are being produced within a country’s borders, by the citizens and the non-citizens. While GNP determines the value of goods and services that are being produced by the country’s citizens in the domestic and abroad spectrum. GDP is popularly used by the global economies at large. While, the United States eliminated the use of GNP in the year 1991, thereby adopting GDP as the measure to compare their economy with other economies.

India’s Richness: National Income of India 2020-2021

In the year 2020-2021, India had a total NI of 135.13 lakh crore, well this is a provisional estimate only. However, in the round of the fourth quarter (in the month of January-March), the country had an economic growth of 1.6%, while the GDP was calculated at Rs. 38.96 lakh crore in the fourth quarter in the year 2020-21, this is count is slightly different to Rs 38.33 lakh crore in the fourth quarter of 2019-20.

In a special type of exchange, the transfer of assets and liabilities occurs with another entity this is called a non-monetary exchange. Real asset swap happens between two organizations that exchange assets of one fixed asset to another.  

The accounting for this non-monetary exchange takes place based on the fair values of the assets that are transferred.  The cost of the recorded non-monetary asset is to be determined which is thus recorded in the following preference: 

• At the fair value of the asset that is transferred in exchange for it. 

• At the fair value of the asset that is received, if the fair value of the asset is more evident than its fair value.

• At the recorded amount of the asset that is surrendered, if no fair values are to be determined.

Non-monetary Transactions Commercial Substance 

The commercial substance of a non-monetary exchange is dependent on the fluctuations of the future cash flows that are expected to be a significant result of the exchange. 

A business transaction that has a commercial substance is expected to have varied cash flows of a business which will change as a result of this transaction. A change in the cash flows is considered to be a significant change in any of the following cases:

• Risk – As like experiencing an increase in the risk which will inbound cash flows, that will occur else than a transaction. 

• Timing – The change in timing of cash inflows that are received as the result of a transaction.

• Amount – Change in the amount that is paid as the result of such a transaction. 

Non-Monetary Exchanges ASC section 845 

ASC 845-10 notes as following:

Generally, the business transactions involve the exchanges of cash or other monetary assets or other liabilities for goods or services. The amount of monetary assets or the liabilities which are exchanged provides an objective basis for measuring the cost of the non-monetary assets or the services that are received by an entity as well as for measuring the gain or loss on non-monetary assets that are transferred from an entity. These transactions involve either of the following:

• Exchange with another entity, also known as a reciprocal transfer which involves principally the non-monetary assets or liabilities.

• A transfer of the non-monetary assets for which no assets are received or are relinquished in exchange is a non-reciprocal transfer.

Both the exchanges and the non-reciprocal transfers which involve little or no monetary assets or liabilities are referred to as non-monetary transactions.

Non-Monetary Transactions 

Nonmonetary transactions are either reciprocal or non-reciprocal. Reciprocal, that is the two-way non-monetary transactions involve more than two or two parties who exchange non monetary goods, services, or assets. Non-reciprocal, which is the one-way non-monetary transactions involving the transfer of goods, services, or assets from one party to another, such as a business that donates the employees.

PIK is the use of a good or service where it is paid instead of cash. This also refers to a financial instrument that pays interest or dividends to the investors of bonds, notes, or the preferred stock. Payment-in-kind securities are attractive to those companies who are preferring not to make cash outlays.

In either case, in-kind transactions are the non-monetary type. For example, farmland that is given a free room and board instead of receiving the hourly wage in exchange for helping out on the farm’s work is an example of payment-in-kind.

 The Internal Revenue Service or the IRS refers to payment-in-kind as bartering of income. The IRS mandates the people who receive payment-in-kind income through bartering to report it on their income tax return. For example, if a plumber accepts a side of the beef loaf in exchange for services, he should report accordingly the fair market value of the beef loaf or his usual fee as income on his income tax return.

Non-Monetary Transactions Journal Entry

Company exchanged a small truck with a book value of Rs.45,000 (cost of Rs.70,000 and accumulated depreciation of Rs.25,000) for a delivery van. A dealer with experience in this market segment told the company that the fair value of the truck is Rs.50,000. The company will also pay Rs.8,000 cash as part of the exchange. This transaction has commercial substance.

The Cost of the Delivery Van is:

The Gain on the Exchange is:

The Journal Entry For Recording the Exchange Will Be:

Online transaction is when we buy any goods online and we pay for those goods online. Everything is safe and secure in online transactions. In this, It happens via confirmation of the OTP sent to your phone, which is very well secured. There is no need to do any kind of paperwork in online transactions. 

There are three stages of online transaction i.e. first – registration, second – placing the order, and third – online payment. This online transaction is completed by combining all three stages. Online transactions are used to buy or sell any item on an online platform such as Flipkart, Amazon, or eBay etc.

Stages of Online Transactions:

There are three stages of online transactions-

Pre-purchase/Sale- The company advertises the product in this stage, it tells about some important things through the advertisement so that the customer can get to know about that product. These advertisements are made in such a way that the customer who is attracted to the advertisement is ready to buy the product.

Purchase / Sale – In this stage, when the customer is attracted to buy goods, he likes the goods, then he buys the goods and he pays online for those goods.

Delivery Stage – In this stage the customer buys the final goods and gets the delivery to the themself.

Steps Involved in Online Shopping (Online Transaction):

The following steps involved in online shopping (online transaction) 

Registration: The first step is registration in online transactions. In this step, the customer has to register himself on a website such as Flipkart, Amazon. To register, he has to provide his email id, name, address and all other similar details, which the website saves and Always keep these details secure and only. After registering on the website, an account is created and he has a shopping cart, both these things are password-protected.

Placing an Order: In this, the customer puts whatever items he likes from his registered shopping website in the shopping cart. This shopping cart then keeps the details of all the items saved, such as how much money it is in, how much is in the amount, it saves all the things with the shopping cart. Then whenever the customer has to order those things, by paying online, he can get all those things.

Payment: The buyer gets a lot of options for placing orders, which are safe and secure, the payment options that are available here are very secure, they have high-level encryption so that the financial details of the buyer cannot be leaked like his/her card number, his/her bank account number, his/her password, all these things could not be leaked. Below are some payment methods in which the buyer can choose how to pay.

Cash on Delivery:  In cash on delivery, the customer pays wherever he wants his product to be delivered. He can make the payment from any method, whether it is through card or cash.

Cheque: In this step, after selecting the cheque option in the payment method, the payment is made in the cheque. First, the customer has to send the cheque to the seller and when the seller withdraws the cash from the cheque then he sends the goods to the customer whatever he ordered.

Net Banking Transfer:  Payment in this step is from the buyer’s account. First, the buyer transfers money through electronic methods to the seller’s account. When that money comes from the seller’s account, then the seller dispatches the product to the buyer’s address.

Credit or Debit Card:  In this step, the buyer has to share the details of his credit or debit card with the seller. When the buyer shares his details with the seller, the seller extracts the specific amount of money from the buyer’s account. The confirmation message for the transaction goes through the OTP to the buyer and then when the buyer enters that OTP, the specific amount is deducted from the buyer’s account. 

Security and Safety of E- Business:

1. Transactional Risks:  The common transactions risks of online dealings are:-

Default an Order- Suppose you bought something online from a site and paid for it, but the seller can deny that you have placed the order or paid for the order. The seller can also refuse to deliver the goods in this way.

Default on Delivery – It often happens that you have placed an order and the product sent to the address of someone else instead of your address (that you have inserted).

Defaulter Payment – It happens very often that the seller does not get the same payment, but the customer who claims that he paid. To avoid this problem, the website provides cookies which are like a personal ID or caller ID which extracts the name, address, and previous purchase records of the customer.

2. Data Storage and Transaction Risk:  Upon registering on a site, we share some personal information on it, such as our name, our address, email ID, phone number. All this information is saved and kept in its data. Due to this, the probability increases that our personal information can be stolen by anyone and can put us at high risk. 

The risk involved in data storage is- Virus (Vital information under siege)- A lot of computer viruses are deadly, which can enter your computer in any way such as through a pen drive, through an email ID, or through a disk, which can enter your computer. All the data present in it, all the important information can be deleted. Because of which you may have a lot of problems and there may be too much time wasted.

Hacking – Hackers are unauthorised people. They can destroy all your data and can also steal it, due to which there is a lot of damage to the website.

3. The Risk of Threat Intellectual Property and Privacy: The information you provide to the website may get copied by any other online vendors, who may start sending you promotional messages and even hackers may pretend to be customers themselves. A fake website may be developed instead of the original website and they take away advance money from customers and not supply any product to the customers.

Risks Related to Online Shopping 

Besides the risks related to data storage, transactions, and threat to privacy, there are some other risks involved with online shopping  too. These are as follows: 

The passing of or transfer of ownership to the buyer is implied by a sale of property or goods. The liabilities and the rights of the buyer and the seller are determined by the help of an important aspect, the passing of property in goods. After the buyer is passed on a property, any risk to the goods sold is not of the seller anymore, rather it solely is of the buyer. This stands true even when the seller possesses the goods. We shall learn more about the passing of property in the Sale of Goods Act 1930. 

Passing of Property

There are four primary rules regarding the passing of property in the sale of goods act 1930.

• The Passing of Ascertained or Specific Goods

• Passing of Unascertained Goods

• Goods are Transferred upon the Basis of Approval or “On Sale or Return”

• Passing of Property in case of reservation of the Right to Disposal

We shall be putting light into the first two rules in this article.

Passing of Ascertained Goods 

Section 19

The first rule of the passing of property in goods deals with the passing of specified goods. It states that specific goods or ascertained goods can only pass when they are intended to pass. There are three subsections under Section 19 of The Sale of Goods Act, 1930 which are as follows.

1. Sub-section (1)

The contract for the sale of ascertained goods clearly mentions the time when the transfer of property is intended by the parties to the contract. The property is transferred only at the time which is expressed in the contract.

2. Sub-section (2)

The terms of the contract, the conduct of the parties and the circumstances of the case are evaluated to determine the intention of the parties.

3. Sub-section (3)

The rules to establish the intention of the parties are given in the Sections 20-24 of The Sale of Goods Act, 1930. The intention is regarding the time at which the property in the goods is supposed to pass to the buyer. We shall learn about these sections in detail.

Section 20

Section 20 deals with ascertained goods in a deliverable state. It pronounces that the property in the goods is transferred to the buyer at the time when the contract is made if the contract is unconditional in nature regarding the sale of ascertained goods in a deliverable state. Such a rule stands true even if the payment of the cost or the delivery of the goods or both are postponed.

E.g., Jack buys a refrigerator from a store and asks them to deliver it to his address and they agree. The refrigerator immediately becomes Jack’s property.

Section 21

Section 21 states that specific goods should be made to be in a deliverable state. In a contract for the sale of goods, if the seller has to get a certain thing done before the goods are ready to be delivered, the transfer of property happens only after the seller completes the task and informs the buyer about it.

E.g., Jill buys a pair of trousers and asks for home delivery and the store agrees. The trousers are longer than needed and the store promises to get them altered and call Jill before delivery. In such a situation, the property passes on to Jill after the store has altered them making them delivery ready. 

Section 22

This section states that the goods might be in a deliverable state but to ascertain the price of the goods, the seller needs to do something extra. A contract of sale of goods which are in their deliverable-state but the seller is supposed to weigh, measure, test or perform a certain action with the goods to specify the price. The property does not pass unless the seller does the mentioned extra act and informs.

E.g., Jack sells a Smart T.V. to Tim and agrees to install it by getting it mounted on Tim’s wall as a part of the contract. Jack delivers the TV and informs Tim that he will install it the next day. The same night, the TV gets stolen from Tim’s house. Here, Tim is not liable for the loss since the ownership of the property had not passed on to him. As per the terms of the contract, the TV would be in a deliverable state only after it is installed.

Passing of Unascertained Goods

Section 18 of the Sale of Goods Act, 1930 states that unless the goods are ascertained, the transfer of the property of the goods to the buyer cannot be completed, under the contract for the sale of unascertained goods.

Section 23

Two necessary rules for the transfer of property of unascertained goods are listed under Section 23. These are:

1. Sale of unascertained Goods by Description

If the sale of unascertained or future goods is described in a contract, the goods with matching description are appropriated to the contract. It is done with either the buyer’s or the seller’s consent. Consequently the property of the goods get transferred to the buyer. The consent of the party here could be clear or implied and given after or before the appropriation is done.

2. Delivery to the Carrier

In some cases, the goods are delivered by the seller to the buyer or a bearer or a bailee (who may or may not have been named by the buyer) for getting it dispatched to the buyer. Here, the seller doesn’t retain the right of disposal. He unconditionally appropriates the goods to the contract.

Some Points to Remember about the Appropriation of Goods

Appropriation of goods is when goods are chosen with the intent to use them in making a contract with the mutual consent of the seller and buyer. Following are some of the requirements.

• There must be an existing contract for the sale of future goods or unascertained goods.

• The quality and the description stated in the contract should be conforming with the goods.

• The goods should be in a deliverable state.

• They should be unconditionally appropriated to the contract by either delivery to the buyer or his trustee or the carrier.

• The appropriation is done by the seller with the consent of the buyer or by the buyer with the consent of the seller.

• The consent could either be expressed or implied.

• The consent could be given before or after the appropriation of the goods.

Solved Question of Passing of Property

Q1. Dave sells goods to Jim that is to be sent over to Jim by air. He makes a bill of lading in the name of Jim. The goods get lost in transit. Would Dave be liable here?

Ans: Since Dave makes a bill of lading in Jim’s name for a package being sent to Jim, the ownership of the goods transfers to Jim. In case of accidental loss, Dave wouldn’t be liable anymore.

Q2. For the Appropriation of Goods, the consent given by the parties has to be expressed. TRUE or FALSE?

Ans: FALSE. The consent given could be of the implied nature too.

Planning is the collection of necessary steps to be taken in order to reach the desired goal. It generally involves thinking and jotting down those steps that will help you in reaching the target. 

For example, your target is to score higher grades in the final exam at school. So, you start with planning on how to do it, for which you start by taking a look at the syllabus. After that, you jot down the necessary step that will help you score higher eventually.

Here, what you think and list down before you start implementing them, is what is planning in simple words. 

Planning Process – What Is It?

Planning in itself is a process that includes multiple steps. According to the planning process definition, one goes through a series of directions during planning.  For instance, suppose your school is conducting a Football tournament and your class teacher has assigned you the task of preparing a school team.

So, what would you do now? You are given two days to finalise your team and give the names to your teacher. Now, you are not aware of who can play well in your class, so you need proper planning to assess who is fit and can be a part of the team.

Now, you call for an assessment round wherein you give a task to evaluate the best members for your team. Therefore, all that you think and list before implementing the same is the process of planning.

Additionally, one should also know that the planning process can be of several types –

• High-level plans

• Short-term plans

• Operation plans

• Assignment plans

While the objective remains common in each of these, as the planning definition does not change in any of them. However, only the requirements vary based on the desired goal, but the process does not change overall.

What Are The Steps of Planning?

As already mentioned, planning is not a standalone concept, but it consists of multiple steps. Here is a brief explanation of the 8 steps planning process for a simplified understanding.

1. Determine Your Objective

The first step in planning is to identify what you want to achieve. Assess your objective if it is a long term or a short term goal. Besides, also check whether the objective is based on external factors such as market fluctuations or not.

As you look for ‘what is planning’, being able to determine all of it specifically will help you in sailing through the next steps smoothly.

2. Sort Tasks That Will Lead To Your Goal

The second step is to divide the whole planning into sub-parts so that executing them becomes easier and the tasks get accomplished faster. It is also essential to list down the tasks that are to be done immediately and segregate the other than might be required later.

3. Identify Potential Resources

Once the task segregation is done, you should now move on to identifying the resources that will fit into the role and help you achieve the target. Know the capabilities of your resources and allocate the task accordingly.

For instance, you will assign the role of a goalkeeper to a person who is tall and has the maximum agility with a quick reflex. On the other hand, you will choose a striker who has good stamina.

4. Check for Alternative Resources

It is always wise to have alternatives, the next step is to check the strength and weakness of the resources that you already have. Based on that, you can look for other resources that can act as a backup if the former resource fails to provide you with the necessary information.

This step is similar to having extra team members, who can come to the field in case one of the team members gets injured or is disqualified in between the match.

5. Sort Out Necessary Techniques

The next step to explain the process of planning is to determine the necessary techniques by which you will go about the implementation of the plan. Find out if you or your resources are familiar with the required techniques.

6. Keep A Progress Tracker

Make sure to have a tracker that will track your proceedings while you execute the plan. Assess whether all your resources are functioning well or if there is any discrepancy. Sort it out once you identify any loophole.

7. Take A Final Look

Now revise the entire plan from the very first step. Ask questions to yourself if all the steps lead you to your desired goal. Be very careful when going through the entire plan. You can also make a checklist of the most essential aspects to avoid missing out.

8. Communicate To The Team Members

This is the last step where you convey the plan to your members for the initiation of the plan. On another instance, if it is solely your task, you can execute the plan finally.

Herein, you start with the first step and proceed one by one. As in the case of your Football team, you can go about assigning a task to everyone interested. Based on their performance, the role can be allocated thereafter. Besides, you also keep a few members beyond the team size as a backup.

For more information on what is planning and its steps, you can refer to our online learning programmes available in our website. The study materials offered by are drafted after rigorous research by eminent faculties.

Data Presenting for Clearer Reference

Imagine the statistical data without a definite presentation, will be burdensome! Data presentation is one of the important aspects of Statistics. Presenting the data helps the users to study and explain the statistics thoroughly. We are going to discuss this presentation of data and know-how information is laid down methodically. 

In this context, we are going to present the topic – Presentation of Data which is to be referred to by the students and the same is to be studied in regard to the types of presentations of data. 

Presentation of Data and Information

Statistics is all about data. Presenting data effectively and efficiently is an art. You may have uncovered many truths that are complex and need long explanations while writing. This is where the importance of the presentation of data comes in. You have to present your findings in such a way that the readers can go through them quickly and understand each and every point that you wanted to showcase. As time progressed and new and complex research started happening, people realized the importance of the presentation of data to make sense of the findings.

Define Data Presentation

Data presentation is defined as the process of using various graphical formats to visually represent the relationship between two or more data sets so that an informed decision can be made based on them.

Types of Data Presentation

Broadly speaking, there are three methods of data presentation:

• Textual

• Tabular

• Diagrammatic

Textual Ways of Presenting Data

Out of the different methods of data presentation, this is the simplest one. You just write your findings in a coherent manner and your job is done. The demerit of this method is that one has to read the whole text to get a clear picture. Yes, the introduction, summary, and conclusion can help condense the information.

Tabular Ways of Data Presentation and Analysis

To avoid the complexities involved in the textual way of data presentation, people use tables and charts to present data. In this method, data is presented in rows and columns – just like you see in a cricket match showing who made how many runs. Each row and column have an attribute (name, year, sex, age, and other things like these). It is against these attributes that data is written within a cell.

Diagrammatic Presentation: Graphical Presentation of Data in Statistics

This kind of data presentation and analysis method says a lot with dramatically short amounts of time.

Diagrammatic Presentation has been divided into further categories:

When a Diagrammatic presentation involves shapes like a bar or circle, we call that a Geometric Diagram. Examples of Geometric Diagram

Simple Bar Diagram

Simple Bar Diagram is composed of rectangular bars. All of these bars have the same width and are placed at an equal distance from each other. The bars are placed on the X-axis. The height or length of the bars is used as the means of measurement. So, on the Y-axis, you have the measurement relevant to the data. 

Suppose, you want to present the run scored by each batsman in a game in the form of a bar chart. Mark the runs on the Y-axis – in ascending order from the bottom. So, the lowest scorer will be represented in the form of the smallest bar and the highest scorer in the form of the longest bar.

Multiple Bar Diagram

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In many states of India, electric bills have bar diagrams showing the consumption in the last 5 months. Along with these bars, they also have bars that show the consumption that happened in the same months of the previous year. This kind of Bar Diagram is called Multiple Bar Diagrams.

 

Component Bar Diagram

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Sometimes, a bar is divided into two or more parts. For example, if there is a Bar Diagram, the bars of which show the percentage of male voters who voted and who didn’t and the female voters who voted and who didn’t. Instead of creating separate bars for who did and who did not, you can divide one bar into who did and who did not.

 

Pie Chart

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A pie chart is a chart where you divide a pie (a circle) into different parts based on the data. Each of the data is first transformed into a percentage and then that percentage figure is multiplied by 3.6 degrees. The result that you get is the angular degree of that corresponding data to be drawn in the pie chart. So, for example, you get 30 degrees as the result, on the pie chart you draw that angle from the center.

Frequency Diagram

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Suppose you want to present data that shows how many students have 1 to 2 pens, how many have 3 to 5 pens, how many have 6 to 10 pens (grouped frequency) you do that with the help of a Frequency Diagram. A Frequency Diagram can be of many kinds:

Histogram

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Where the grouped frequency of pens (from the above example) is written on the X-axis and the numbers of students are marked on the Y-axis. The data is presented in the form of bars.

Frequency Polygon

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When you join the midpoints of the upper side of the rectangles in a histogram, you get a Frequency Polygon

Frequency Curve

 

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When you draw a freehand line that passes through the points of the Frequency Polygon, you get a Frequency Curve.

Ogive 

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Suppose 2 students got 0-20 marks in maths, 5 students got 20-30 marks and 4 students got 30-50 marks in Maths. So how many students got less than 50 marks? Yes, 5+2=7. And how many students got more than 20 marks? 5+4=9. This type of more than and less than data are represented in the form of the ogive. The meeting point of the less than and more than line will give you the Median.

Arithmetic Line Graph

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If you want to see the trend of Corona infection vs the number of recoveries from January 2020 to December 2020, you can do that in the form of an Arithmetic Line Graph. The months should be marked on the X-axis and the number of infections and recoveries are marked on the Y-axis. You can compare if the recovery is greater than the infection and if the recovery and infection are going at the same rate or not with the help of this Diagram.

Did You Know?

Sir Ronald Aylmer Fisher is known as the father of modern statistics.