Question 2: Consider the following: Your boss tells you that the company is cutting costs this year and decreasing your salary by 6%. But next year they will increase your salary by 6%, so your average salary will stay the same. Relative to the starting point, how will your salary change taking into account both adjustments?

Correct Answer: C

Explanation: Here, you have to remember that percentages work. If your salary decreases by 6%, let’s say from 100 to 94, then increasing the new salary by the same percentage results in a lower amount. Why? This is because increasing from 94 by 6% results in a figure smaller than 100 i.e. your starting point because the increase in from a lower base. Might sound simple, but confuses people nevertheless sometimes.

Question 3: A small liberal arts college has announced that 50% of the men studying Biology were infected by an unknown airborne virus while only 5% of the women who study Biology were infected. The Dean of Students has launched an investigation into why so many more men have been infected. What comparison figure are we missing to figure out whether the Dean's actions are justified?​

Correct Answer: C

Explanation: Here, a similar concept gets tested here, that percentages are always used relative to a certain base. Suppose that 2 men study biology, so 50% is 1 man who got infected and at the extreme let’s say 100 women study biology, so 5% of that is 5 women who got infected. So still more women than men got infected in this hypothetical example, yet, the Dean of Students jumped to the conclusion thinking there were many more men who got infected.

Question 4: A reputable consulting company publishes its research about the travel industry and shows the portion of sales of major companies in 2018. Choose all that apply.

Correct Answers: B, C

Explanation: This one is tricky but very common. The 3D effect skews the true dimensions. The chart on the right is the one should have been used; yes I assure you that the two graphs are identical. Take a look at the green portion of the pie, very similar to the blue portion; so B is correct. C is correct as as well, as a general rule, in a 3D graph, the closer objects appear bigger. So next time you see or pie or bar chart that is 3D, beware.

Question 5: Three vaccines have been developed to tackle a new virus. You are asked to evaluate their efficacy using the following graph. Using only the information in this graph, which one of the following applies?

Correct Answer: B

Explanation: This graph hides a little trick that it has axes with different scales. Since vaccine three results refer to the left axis, it is the most effective. The other two refer to the right axes.

Question 6: ​A prominent journal surveyed 1500 companies on whether they plan to raise their prices next year. 34% of them answered yes, 46% answered no. What should be the conclusion from the survey?

Correct Answer: D

Explanation: There are more sophisticated methods to determine how confident we are about the conclusion but based on the information here, we simply don’t know and need more information and we should not jump to conclusions. We don’t know what the rest of the 19% of companies did . Also, beware of someone telling you phrases like “a prominent journal.” They should cite the source and even then you should still think critically.

Question 7: Jim is playing a five-round game of dice, and in order to win he needs to roll a 6 at least once. After four rounds, he still hasn’t rolled a 6. He thinks he can’t have bad luck for all five rounds. He must have better chances this round. Do you agree?

Correct Answer: B

Explanation: Always remember; when playing with fair dice, the past does not matter. The fact that you roll a six does not mean that your are more or less likely to roll a 6 or any other number next time.

Question 8: Suppose that you see the following graph in your local town's newspaper. Using only the information displayed below, which of the following headlines is an accurate conclusion from the graph?

Correct Answer: B

Explanation: This is another base effect question. If a 3% increase represents $1500 and a 6% increase $2400, then you can conclude that the current salaries of in Our Town are higher.

Question 9: Choose which of these statements if any HAVE a logical flaw in them, make you skeptical about the data, or are misleading. Choose all that apply.

• Statement 1: A town has 1000 people and they have all been asked to assess their driving ability. 64% of them reported that they think they are better than the average driver.

  MISLEADING: The “average” driver is hard to define but overall, it is often the case that people are overconfident in their abilities. By the average driver, we mean the ‘median driver’, the person whose driving ability is in the middle of the pack. But you cannot have 64% of people better than the average driver. You can take it to the extreme where 90% of people they are better than the average driver but that cannot be the case, 50% of people are better and 50% are worse than the middle person.

• Statement 2: A prominent journal surveyed 90 college students on whether they are planning to buy a car. 34 answered yes, 41 answered no. So most students will not be buying a car.

  MISLEADING: Why? Because we don’t know what the remaining 15 students are planning to do. There are more sophisticated methods to determine how confident we are about the conclusion but based on the information here, we simply don’t know and need more information and we should not jump to conclusions.

• Statement 3: The attacker in 71% of all violent crimes is a friend or family member of the victim. This means that you are safer outside than in your own home.

• MISLEADING: This statement makes the wrong conclusion. The statistic could be true because most people you are exposed to are your family, friends or your immediate circle. So you spend most time with them so the chance that this happens is not low. But you should compare with a scenario if you spent the same amount of time with strangers, in that case, the percentage would probably be even higher.

• Statement 4: The National Weather Association reported that in January of 2014, New York City received exactly 1,650,332.4562 pounds of snow.

• MISLEADING: This is an example of excessive precision; it is difficult to imagine that someone can measure the amount of snow that precisely. Generally, be aware of situations when someone quotes a very precise figure like the one above.

Question 10: This chart shows how both radio waves and the number of cancer cases increased in the 1930s. What is the likely explanation for this? Select one answer choice.

Correct Answer: C

Explanation: This is the common correlation-is-not-causation question. In this example, it is “time” as a variable that is common to both radio waves and cancer cases. There can be so many reasons why cancer cases rose during the period in the graph; maybe detection got better, maybe it is simply because population was increasing. The graph does not really specify how we measure radio waves? There are no units really.

Question 11: ​In the winter of 2010, Greater Lake had an average ice depth equal to 2 feet which was considered safe at the time. 11 people died that year as a result of drowning. In 2009, no one died while the average depth was much smaller, 1.3 feet. Which of these would be relevant points to consider here? Choose all that apply.

Correct Answer: B, C, D

Explanation: Since the ice can be thin anywhere on the lake, the average may not necessarily be a good measure. Other factors can certainly be at play here, maybe people were less responsible despite the ice being considered safe. The depth of ice in 2008 is not really helpful in explaining anything here.

Question 12: ​Long jumpers in the Olympics between 2010 and 2020 improved their record by 1m. Using this relationship, long jumpers are expected to improve their record by 4m by year 2060. Is there any ISSUE with this scenario from the perspective of athlete improvement?

Correct Answer: C

Explanation: This example makes one assumption that is important to keep in my mind; it assumes that athlete improvement is linear, that is that the athlete’s result’s will improve proportionally regardless of the starting point. But there are certainly biological limits and the level of improvement probably depends on the starting point a lot.

Question 13: The following electricity companies are selling their services to homes in a local town. The graph below shows the price of electricity that each company offers. Assume that customers really care about the price of electricity being as stable as possible. Which of these companies offers the most stable price for electricity?

Correct Answer: F

Explanation: All three graphs are the same; their axes were adjusted to confuse you. The only thing that is different in each graph is the scale and starting point of the y-axis.

Question 14: Choose which of these statements are misleading or make you skeptical about the conclusion. Choose all that apply.​

• Statement 1: A TV commercial asserts that 10 out of 10 doctors recommend a particular drug to cure a rash.

  MISLEADING: You need to know how those doctors were chosen, are they all unbiased? You can probably find 10 out of 10 doctors who do not recommend the drug.

• Statement 2: 25 countries have improved their dental care more than the US over the past 10 years. Therefore, the state of US dental care is inadequate.

  MISLEADING: This example does not consider the stating point. It focuses on improvement (to the extent that it can be measured) but does not consider the “level” of care. It is something like saying that over past years I have improved more in golf than Tiger Woods. By this logic, the example would claim that Tiger Wood’s golf ability is inadequate.

• Statement 3: Everybody knows that drinking milkshakes causes stomach problems.

• MISLEADING: This is another correlation-causality example; while this may certainly happen, there are many other factors and it is difficult to establish that milkshakes are really the reason for stomach problems. Beware of the "misleading statement “everybody knows”.

• Statement 4: An Italian restaurant has introduced new items to its menu. After a couple weeks, sales skyrocket. The addition of the new menu items caused this increase in business.

  MISLEADING: This is another correlation-causality example; the main question is, how do we know that it was really the menu items? Other factors can be at play here. What if sales increase was caused by the arrival of a big wave of tourists? It is certainly possible, but claiming that the the menu items “caused” the increase in business is premature. It may be useful here to see what happened to other restaurants in the area.

• Statement 5: A department store says that 1.5 million people buy their $3 razor. Only 5% of those who bought a razor used the customer refund option. Therefore, it is clear customers are very happy with the product.

  MISLEADING: This is misleading because we cannot conclude that customers are happy. What if many customers are unhappy and simply do not use the refund option because it is a relatively cheap product?