Numbers having digits to a number divisible by the original number are Harshad numbers. Harshad means 'giver of joy'.

What Is My Number?

Like 420=》 4+2+0=6420÷6=70420 is a Harshad Number.Like 111=》 1+1+1=3111÷3=37111 is a Harshad number.485=》 4+8+5=17485÷17=28.5294....485 is not a Harshad number.

Examples

A handful of numbers have a very special property: you can add their digits together and divide the original number by their total without a remainder. And why does it matter? Well, in terms of mathematics, it's mostly a curiosity. Dattatreya Ramchandra (D. R.) Kaprekar saw these numbers as sparking joy in the mind, so he named them "Harshad" numbers, with harshad being the Sanskrit word for joy. And it's an important lesson about numbers: not every bit of math needs to change the world. Something that makes you go "huh" for a brief moment can be enough. #shorts

Happiness

420 is a Harshad Number #shorts

Averages, relationships, trends and graphs are not what they seem. Statistics can make an important fact look as if it is nothing noteworthy and a trivial fact like there may be more in it. Writers need statistical methods and statistical terms when reporting data of social and economic trends, but they need to use the words honestly, and readers need an understanding of what they mean. Otherwise, it may result in semantic absurdity.

The abused statistic

“The secret language of statistics, so appealing in a fact-minded culture, is employed to sensationalize, inflate, confuse, and oversimplify.”

For any statistic to be worth it, it should come from a representative sample of the group it is describing. But a representative sample is near impossible because of lack of time, resources, and other practical reasons. As a result, you are more likely to see a subset based on biases from the method of sampling rather than the representative group itself. When you see the statistic that, for example, represent the entire nation, ask yourself, “Which part of the nation?”

The representative sample

There are three common kinds of average: 
<ol>
<li>Mean. Add up all the values and divide by the quantity of the values.</li>
<li>Median. The value in the middle of the sample.</li>
<li>Mode. The most common value. </li>
</ol>
When a statistic cites the “average”, it could be the mean, median or mode, which can be drastically different. The unspecified “average” is used to prove a point while leaving out any numbers that might question their predetermined point.

The kind of average

If you want to use a test to measure something or somebody, it is equally important to know the limitations of the test. What can it not measure?  For example, an intelligence test does not measure leadership, creative imagination, diligence, and emotional balance. The test may still be useful for admission to a university or a job, but you should also understand its limitations.

Consider what it really measures

“As long as the errors remain one-sided, it is not easy to attribute them to bungling or accident.” Statistics are often used to support a cause or agenda a person believes in, rather than to disprove them. When people err in their use of statistics, it is always in the direction of their beliefs or agenda. So, instead of getting an unbiased view of the world, we get a biased view that other people want us to see.

Statistics are always biased

“‘Does it make sense?’ will often cut a statistic down to size when the whole rigmarole is based on an unproved assumption.” Consider what they are saying and why they are saying it. If a statistic doesn’t seem right, or someone arrives at a conclusion that seems questionable, ask “Does it make sense”.

The common-sense test

It describes using one thing as a way to claim proof of something else, even if there exists no correlation between the two.Meaningless statements:<ul><li>“32% of doctors think Mercedes vehicles are safe."</li><li>“27 % of a large sample of eminent physicians smoke Throaties— more than any other brand.”</li></ul>Expressing the data to suit your view. For instance, express exactly the same fact by calling it a one % return on sales, a fifteen % return on investment, a ten-million-dollar profit, or a decrease of sixty % from last year.

The semidetached figure

If B follows A, then A has caused B.For example:<ul><li>Assuming that since smoking and low grades go together, smoking causes low grades.</li><li>If you attend college, you will earn more money than if you decide to use the next four years in another way. The unwarranted assumption is that since college-trained people make more money, they make it because they went to college. However, we don’t know if these people would have made more money had they not gone to college.</li></ul>

Correlation vs. Causation

<ol><li>Who says so? What is the agenda? Who will benefit from presenting the data that way? Does it tell the whole story or only the good or bad part? Does it misuse average? Does any bias come into play?</li><li>How do they know? Where did the data come from? Is it representative? Can it be biased? Is the sample big enough?</li><li>What’s missing? </li><li>Did someone change the subject between the raw data and the conclusion? Is it a real statistic, or what someone reported?</li><li>Does it make sense? Pay attention if it fails the common sense test. Is something complex reduced to a single number?</li></ol>

How to avoid blind belief in statistics

This book lays the groundwork for the many ways statistics are used to mislead people. Honest people must learn the tricks of statistics so that they can interpret data intelligently.

Over Half a Million Copies Sold--an Honest-to-Goodness Bestseller Darrell Huff runs the gamut of every popularly used type of statistic, probes such things as the sample study, the tabulation method, the interview technique, or the way the results are derived from the figures, and points up the countless number of dodges which are used to full rather than to inform.

Stashed ideas

How to Lie with Statistics

Financially intelligent managers understand the four distinct skill sets:<ol><li>The Foundation. They can read an income statement, a balance sheet and a cash flow statement. Can differentiate between profit and cash.</li><li>The art of finance. They can identify the artful aspects of finance and know how applying them differently can lead to different conclusions.</li><li>Analysis. They use ratios, return on investment (ROI) analysis, etc. to make better decisions.</li><li>The big picture. Numbers can’t (and don’t) tell the whole story. Financial results should be understood within the framework of the big picture.</li></ol>

Four skill sets of finance and accounting

The art of accounting is taking a limited set of data to get an accurate description of how well a company is doing. Definitions to understand.<ul><li>Revenue is when a service/product is delivered.</li><li>The income statement shows sales/revenues, costs/expenses, and profit. You can often tell what’s important to a company by looking at the biggest numbers relative to sales.</li><li>Operating Expenses: Day-to-day costs needed to keep the business going, e.g., salaries.</li><li>Capital Expenditure: The cost of purchasing an item is considered a long-term investment, such as computer systems or equipment.</li></ul>

You can’t always trust the numbers

Accountants use accruals and allocations to attempt an accurate picture of the business for a month.<ul><li>Accruals: An accrual is the part of a revenue or expense item that is recorded for a specific period, e.g., product development costs. The purpose is to match costs to revenues in a given timeframe.</li><li>Allocations: Theses are apportionments of costs to different departments or activities in a company.</li><li>Depreciation: Allocated cost of equipment and other assets to the total cost of product and services shown on the income statement.</li></ul>

Spotting assumptions, estimates, and biases

Understanding how the numbers are used and what are assumptions puts you in control of the decisions. <ul><li>Goodwill: The difference between the net assets acquired and the amount of money the acquiring company pays form them.</li><li>Balance sheet: The balance sheets show the assets, liabilities, and owners’ equity.</li><li>Cash shown on a balance sheet is money in the bank and things like stocks and bonds that can be turned into cash.</li></ul>

Reason for increasing your financial intelligence


It consists of three main categories:<ul><li>Sales or revenue during a given time period. It includes sales (revenue) and Earnings-per-share (EPS)</li><li>Costs and expenses: “Above the line” are the cost of goods sold (COGS), cost of services (COS). “Below the line” are operating expenses, interest, taxes, depreciation and amortization.</li><li>Profit: Profit is an estimate. You can’t spend estimates. </li></ul>Different kinds of profit:<ul><li>Profit = Revenue - expenses</li><li>Gross profit = Sales - COGS</li><li>Operating profit (EBIT) = Gross Profit - Operating expenses</li><li>Net Profit = Operating Profit - (interest + taxes + other costs)</li></ul>

Cracking the code of the Income Statement

A balance sheet shows what a business owns at a particular time. A balance sheet always balances. Assets = liabilities + owners’ equity.<ul><li>Assets: What the company owns. It is more estimates and assumptions. Assets include cash; accounts receivable; inventory; property, plant, and equipment (PPE) minus accumulated depreciation; goodwill; intellectual property, patens; accruals.</li><li>Liabilities: What the company owes.</li><li>Equity: The assets - liabilities.</li></ul>

Understanding the balance sheet

A good manager is aware of how both cash and profits affect a balance sheet. A balance sheet shows if a company is financially healthy. The balance sheet answers the following questions:<ul><li>Do the assets outweigh the liabilities?</li><li>Can the company pay its bills?</li><li>Is the owner’s equity growing?</li></ul>

The income statement always affects the balance sheet

Profit is not cash. A healthy business needs both profit and cash. Inflows: Cash moving into a businessOutflows: Cash moving out of a business Types of cash flow:<ul><li>Cash from operating activities</li><li>Cash from investing activities</li><li>Cash from financing activities</li></ul>Financing a company: Getting a company the cash it needs to start up or expand. Cash flow can be calculated by looking at the income statement and two balance sheets. When you know a company’s cash situation, you can understand what’s going on now, where the business is headed, and the priorities of senior management.

The language of cash flow

Explains what business numbers mean and why they matter, and addresses issues that have become more important in recent years, including questions about the financial crisis and accounting literacy.

420 is a Harshad Number #shorts

How to Lie with Statistics

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