Benford’s law

Benford’s law is an observation about the leading digits of the numbers found in real-world data sets. Intuitively, one might expect that the leading digits of these numbers would be uniformly distributed so that each of the digits from 1 to 9 is equally likely to appear. In fact, it is often the case that 1 occurs more frequently than 2, 2 more frequently than 3, and so on. This observation is a simplified version of Benford’s law. More precisely, the law gives a prediction of the frequency of leading digits using base-10 logarithms that predicts specific frequencies which decrease as the digits increase from 1 to 9.

It is used often in Applications to Fraud Detection

It is difficult for humans to manually construct distributions that satisfy Benford’s law. Fraudulent numerical data can often be identified by simply looking at the frequency of first digits, although often in practice more than one digit is used for a more precise check. In particular, Benford’s law has been applied to entries on tax forms, election results, economic numbers, and accounting figures.

This phenomenon occurs generally in many different instances of real-world data. It becomes more pronounced and more likely when more data is combined together from different sources. Not every data set satisfies Benford’s law, and it is surprisingly difficult to explain the law’s occurrence in the data sets it does describe, but nevertheless it does occur consistently in well-understood circumstances. Scientists have even begun to use versions of the law to detect potential fraud in published data (tax returns, election results) that are expected to satisfy the law.

Here is a histogram of the areas of 196 196 196 countries (data taken from Wikipedia). The units are km2 \text{km}^2 km2.

Here is a table with percentages. The “BL prediction” column is the percentage that Benford’s law predicts for each digit. (These numbers will be explained in the full statement of the law in the next section.)

First digitNumber of countriesPercentageBL prediction

Here is a histogram of the population of each of the 3,142 counties or county equivalents in the United States (data taken from Wikipedia).

Here is a table with percentages.

First digitNumber of countiesPercentageBL prediction

So Benford’s law appears to predict the data in both examples quite well.


I’m not going to explain here how the law work.

However when using big number this is a marvelous way to create application for checking anomalies in a set of data .

Not well advertised as tool and ditto here it is!

Google its’ watching you

Google is a corporation. Their goal is to acquire as much of the world’s money as possible.

Scott Cleland, who has made a career of watching Google and ringing the “seriously, I think these people might be vampires” alarm, “Google does not work for users; Google works for advertisers and website publishers, which provide virtually all of Google’s revenues.” Google Ads are responsible for 97 percent of their billions of dollars of revenues.

Everything Google has ever given you for free is funded by those little blue lines of text that appear at the top of your Gmail account, or in the sidebar of your search results. Then, when you use those services, Google collects information about you. It uses what it knows about you to target ads specifically to your personal tastes. That’s how Google is able to maintain a near monopoly in online advertising.

Additionally you use Google for searches at least once in your life so:

It turns out, Google records everything you enter into its search engine. The lonely night a few months back when you Googled “how many fists can fit in the butt?” That’s stored on Google’s servers, correlated with your IP address and a pretty shocking amount of other personal information.

Unless you live under a rock, you’ve heard that Google is buying connected device maker Nest.

However, what you might not know is how Google could use Nest’s products in the future to track your every move. The search giant, after all, is known for its proficiency in collecting and mining user data. And what better way of doing this than through in-home devices such as Nest’s smart thermostat or smoke detector?

Acquiring Nest gives Google an entry into the burgeoning “Internet of Things” — a market that’s expected to be worth $14.4 trillion over the next decade, according to Cisco. If you’re not yet familiar with the term, it refers to the growing network of machines, appliances, and everyday objects, which are being connected and controlled through the Web today.

If you use Google to help you navigate the Web, there’s a good chance they’ve installed a cookie onto your browser that logs every page you visit, every form you fill out and every conversation you have. Google sees it all and stores it for at least nine months.

Consumer advocate group Privacy International says nine months is the best case scenario. Even if you only use a few of Google’s free services, “the company retains a large quantity of information about that user, often for an unstated or indefinite length of time, without clear limitation on subsequent use.”

And now surely they do not need a cookie on your computer!

Google knows a lot more about you than you probably think it does.

If you use its products, such as Gmail, Google Search or even an Android phone, the company is collecting your data to make its services better for end users. CNBC recently showed you how to discover what Facebook knows about you, so now we’re back with data on what Google knows, too.

It’s not hiding that it knows this — a quick peek at its privacy policy makes it crystal clear that Google knows this information — but it might be surprising just how much it knows.

As a quick sampler, while I worked on this guide, I discovered Google knows the following about me:

    My name, gender and birthdate

    My personal cellphone numbers

    My recent Google searches

    The websites I’ve visited

    That I turned on my bedroom lights last night

    Exactly where I’ve been over the past several years

    That I like American football, games, jazz, audio equipment, my favorite food & drink and more.

    Where I work

    Where I live

    The YouTube videos I’ve watched and my YouTube searches

    Every time I’ve used my voice to interact with Google Assistant (complete with recordings of my voice.)

Scary isn’t it?

How much Google actually knows about you? In reality, noone really knows (or is willing to share with the public), but you can find out a lot, if you only know where to look.

The Dashboard– Login to your Gmail account (if you are not logged in already) and visit your personalized Dashboard.

The Location– If you have any sort of an Android device (phone or tablet) you were asked when you set it up initially if you are OK with your device transmitting location information back to the mother ship. If you said yes, here is this information.

Search History-Unless you have explicitly opted-out from Google keeping track of your search history, you can find all the data they have on your searches here.

Knowledge is power. Google has the knowledge, you have the power to use it to become a high performer.

Learn Social Engineering

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