This page describe very interesting statistics and math curiosities that may surprise you ! PROOF THAT 1 EQUALS 2 Proof: Description: [1] We start with: a=b;  [2] Multiply both sides by “a”: a^2=ab; [3] Subtract b squared from both sides: a^2-b^2=ab-b^2; [4] Factorize: (a+b)*(a-b)=b(a-b) [5] Divide both sides by (a-b): ((a+b)*(a-b))/((a-b) )=(b(a-b))/((a-b) )  [6] So we have: (a+b)=b [7] Because we said a=b in the first step: (b+b)=b [8] Dividing both sides: 2b/b=b/b [9] Finally: 2=1 (Cool !) The problem is in step 5. If a=b, then a-b=0 should not be in the denominators… THERE ARE FAR LESS STARS THAN TREES According to statistics, there are more trees on Earth than there are stars in the Milky Way. Today, there are around 3 trillion trees and 400 billion stars. (brightside.me) THE PEOPLE’S REPUBLIC OF CHINA IS KNOWN AS, “THE GOLDEN REPUBLIC” There is more gold in China than in any other country. Research has found that 440 tons of gold are mined in China every year. (brightside.me) EVERY CLICK, EVERY VIEW AND EVERY SIGN-UP ON INTERNET IS RECORDED SOMEWHERE Depending on your view, this is either very creepy or fantastically interesting.  As we’re data nerds here at Brandwatch we fall firmly in the second camp. We come across all sorts of interesting stats about social media sites and users, so we’ve collated the best of them in these bumper facts list. And it comes as a great fact sheet to give context to your social media marketing efforts. For the curious, these represent a series of numbers that boggle the mind, users counted in tens and hundreds of millions, and time in millions and billions of hours. For marketers, knowing the statistics behind the social networks can inform strategy and spend, allowing focused targeting of users. (brandwatch.com) IN THE U.S., 1,700 PEOPLE BECOME MILLIONAIRES EVERY DAY There are many more millionaires in the world than you might think. In the U.S., 1,700 people become millionaires every day. According to statistics, in the U.S., there are more than 8 million families whose yearly income is more than $1 million — and this number doesn’t include any property or jewelry. (brightside.me) MCDONALD’S SELLS 75 BURGERS PER SECOND One of the most popular fast food restaurants, McDonald’s sells around 75 burgers a second. They even have a special website which can help you track how many products have been sold and how many clients have been served. (brightside.me) NUMBERS FROM BIG TECH COMPANIES 4Chan: 27.7 million users Airbnb: 150 million users Facebook: 2.072 billion users Flickr: 90 million users Google+: 111 million users Instagram: 800 million users LinkedIn: 500 million users MySpace: 15 million users Periscope: 10 million users Pinterest: 200 million users Reddit: 234 million users Snapchat: 178 million daily users Twitter: 330 million users Wechat: 1.12 billion users Weibo: 600 million users WhatsApp: 900 million users Youtube: 1.5 billion users (brandwatch.com) YOU MAY WALK AROUND EARTH 4.5 TIMES DURING YOUR LIFE On average, a person makes 7,500 steps a day with an average life expectancy of 80 years. Using this data, scientists calculated that a person can walk 180,000 kilometers during their lifetime. This means that in your life, you can walk around the equator 4.5 times. (brightside.me) SOCIAL MEDIA STATISTICS For context, as of April 2018, total worldwide population is 7.6 billion The internet has 4.2 billion users There are 3.03 billion active social media users On average, people have 5.54 social media accounts 91% of retail brands use 2 or more social media channels 81% of all small and medium businesses use some kind of social platform Internet users have an average of 7.6 social media accounts Social media users grew by 121 million between Q2 2017 and Q3 2017. That works out at a new social media user every 15 seconds. Facebook Messenger and WhatsApp handle 60 billion messages a day (brandwatch.com) FOR THE PAST THOUSAND YEARS, EARTH’S POPULATION HAS GROWN 22 TIMES BIGGER The population of Earth has grown more than 22 times from the year 1000 to 2000. In July of the year 1000, there were 275,000,000 people; and in July of the year 2000, there were 6,145,006,989 people. (brightside.me) GERMANY’S POPULATION HAS THE LOWEST PERCENTAGE OF CHILDREN Children aged 0 to 14 years make just 12% of the population of Germany, whereas in Kenya the same age group makes up 40% of the population. (brightside.me) HOW MANY PEOPLE ARE BORN/DIE EVERY DAY IN THE WORLD? 19 births/1,000 population 8 deaths/1,000 population 131.4 million births per year 55.3 million people die each year 360,000 births per day 151,600 people die each day 15,000 births each hour 6,316 people die each hour 250 births each minute 105 people die each minute Four births each second of every day Nearly two people die each second    Average life expectancy at birth is approximately 67 years. (Population Reference Bureau & The World Factbook -Central Intelligence Agency; quora.com) GOOGLE STATISTICS Google processes 100 billion searches a month That’s an average of 40,000 search queries every second 91.47% of all internet searches are carried out by Google Those searches are carried out by 1.17 billion unique users Every day, 15% of that day’s queries have never been asked before Google has answered 450 billion unique queries since 2003 60% of Google’s searches come from mobile devices By 2014, Google had indexed over 130,000,000,000,000 (130 trillion) web pages To carry out all these searches, Google’s data center uses 0.01% of worldwide electricity, although it hopes to cut its energy use by 15% using AI (brandwatch.com) SOCIAL VIDEO STATISTICS Facebook now sees 8 billion average daily video views from 500 million users Snapchat users also sees 8 billion average daily video views US adults spend an average of 1 hour, 16 minutes each day watching video on digital devices Also in the US, there were 175.4m people watching digital video content 78% of people watch online videos every week, 55% watch every day It’s estimated that video will account for 74% of all online traffic in 2017 (brandwatch.com) FACEBOOK STATISTICS Facebook adds 500,000 new users every day; 6 new profiles every second 68% of all Americans are on Facebook 79% of all online US adults use Facebook 76% of Facebook users check it every day The average (mean) number of friends is 155 Half of internet users who do not use Facebook themselves live with someone who does Of those, 24% say that they look at posts or photos on that person’s account There are an estimated 270 million fake Facebook profiles (brandwatch.com) THE TOP 10 CAUSES OF DEATH Of the 56.9 million deaths worldwide in 2016, more than half (54%) were due to the top 10 causes. Ischaemic heart disease and stroke are the world’s biggest killers, accounting for a combined 15.2 million deaths in 2016. These diseases have remained the leading causes of death globally in the last 15 years. Chronic obstructive pulmonary disease claimed 3.0 million lives in 2016, while lung cancer (along with trachea and bronchus cancers) caused 1.7 million deaths. Diabetes killed 1.6 million people in 2016, up from less than 1 million in 2000. Deaths due to dementias more than doubled between 2000 and 2016, making it the 5th leading cause of global deaths in 2016 compared to 14th in 2000. Lower respiratory infections remained the most deadly communicable disease, causing 3.0 million deaths worldwide in 2016. The death rate from diarrheal diseases decreased by almost 1 million between 2000 and 2016, but still caused 1.4 million deaths in 2016. Similarly, the number of tuberculosis deaths decreased during the same period, but is still among the top 10 causes with a death toll of 1.3 million. HIV/AIDS is no longer among the world’s top 10 causes of death, having killed 1.0 million people in 2016 compared with 1.5 million in 2000. Road injuries killed 1.4 million people in 2016, about three-quarters (74%) of whom were men and boys. (www.who.int) WORLD GDP PER CAPITA Three lists of countries below calculate gross domestic product (at purchasing power parity) per capita, i.e., the purchasing power parity (PPP) value of all final goods and services produced within a country in a given year, divided by the average (or mid-year) population for the same year. As of 2017, the average GDP per capita (PPP) of all of the countries of the world is USD $17,300. Complete list: https://en.wikipedia.org/wiki/List_of_countries_by_GDP_(PPP)_per_capita WORLD GDP Gross domestic product (GDP) is a monetary measure of the market value of all the final goods and services produced in a period (quarterly or yearly) of time. Nominal GDP estimates are commonly used to determine the economic performance of a whole country or region, and to make international comparisons. Nominal GDP per capita does not, however, reflect differences in the cost of living and the inflation rates of the countries; therefore, using a basis of GDP per capita at purchasing power parity (PPP) is arguably more useful when comparing differences in living standards between different nations. Per the International Monetary Fund (2017): Complete list: https://en.wikipedia.org/wiki/List_of_countries_by_GDP_(nominal) WORLD INEQUALITY-ADJUSTED HDI This is a list of countries by inequality-adjusted human development index (IHDI), as published by the UNDP in its 2016 Human Development Report. According to the 2016 Report, "The IHDI can be interpreted as the level of human development when inequality is accounted for," whereas the Human Development Index itself is "an index of potential human development (or the maximum IHDI that could be achieved if there were no inequality). Complete list: https://en.wikipedia.org/wiki/List_of_countries_by_inequality-adjusted_HDI THE MONTY HALL PROBLEM Say you're on a game show where there are three doors. Behind two of the doors, there are goats. Behind one of the doors, there is a brand new car. The host says that once you pick a door, he'll open one of the doors you didn't pick to reveal a goat. Then, you have the option of either staying with your door or switching to the last unopened door. Do you switch or stay? Answer: Switch This is actually based on a real game show, and the result has been the source of controversy for years. Essentially, when you first made the selection, you had a one in three chance of correctly selecting the door that had a car behind it. Switching raised that probability to two in three that you'll select a car. Said another way: A player whose strategy is to always switch will only lose when the door they initially selected has a car behind it. A contestant who selects either of the two doors with a goat behind it and then switches will always get the car. Here's a final way to look at it, provided the contestant selected Door #1 Door 1 Door 2 Door 3 Result if Stay #1 Result if Switch Car Goat Goat Car Goat Goat Car Goat Goat Car Goat Goat Car Goat Car (straightdope.com) SIMPSON'S PARADOX It is a phenomenon in probability and statistics, in which a trend appears in several different groups of data but disappears or reverses when these groups are combined. Example: A kidney study is looking at how well two different drug treatments (A and B) work on small and large kidney stones. Here is the success rate that was found: Small Stones, Treatment A: 93%, 81 out of 87 trials successful. Small Stones, Treatment B: 87%, 234 out of 270 trials successful. Large Stones, Treatment A: 73%, 192 out of 263 trials successful. Large Stones, Treatment B: 69%, 55 out of 80 trials successful. All stones, Treatment A: 78%, 273 of 350 trials successful. All stones, Treatment B: 83%, 289 of 350 trials successful. Which is the better treatment, A or B? Answer: Treatment A, once you focus on the subsets. Even though Treatment A had higher success rates in both small and large stones, when the whole trial is viewed as a sample space Treatment B seemed more successful: Small Stones, Treatment A: 93%, 81 out of 87 trials successful Small Stones, Treatment B: 87%, 234 out of 270 trials successful Large Stones, Treatment A: 73%, 192 out of 263 trials successful Large Stones, Treatment B: 69%, 55 out of 80 trials successful. All stones, Treatment A: 78%, 273 of 350 trials successful All stones, Treatment B: 83%, 289 of 350 trials successful. This is an excellent example of Simpson's Paradox, where correlation in separate groups doesn't necessarily translate to the whole sample set, causing ambiguity. In short, just because there correlation in smaller groups hides the real story taking place in the largest of groups. (businessinsider.com) DON'T LET THE P-VALUE MAKE YOU A FOOL! In a hypothesis test, if p-value = 0.05, what is the probability of rejecting H0 incorrectly? Answer: 5% (this is the wrong answer!); 50% (good chance of being the right answer). Believe: For p-value = 0.05, the probability of rejecting H0 incorrectly is at least 23% (and typically close to 50%). Maybe it's time to rethink your hypothesis tests. Take the time to take a look at www.dunamath.com! Reference: Sellke, T., Bayarri, M. J., & Berger, J. O. (2001). Calibration of ρ values for testing precise null hypotheses. The American Statistician, 55(1), 62-71. See more in our group: