One of the skills that’s being tested during a case interview is something I call data sufficiency.
Basically, you have a bunch of data and the question is do you have ENOUGH data to make a particular conclusion.
This is certainly something that is tested during a live, in-person, face-to-face case interview.
It is also a skill that is often tested in a variety of formats including written tests before the first in-person case interview question is asked.
An example of this is the McKinsey Problem Solving Test which evaluates your data sufficiency skills (among others).
In parts of the McKinsey Problem Solving Test, you are given a bunch of data and some possible conclusions.
Your job is to figure out which conclusions are or are NOT supported by the facts presented.
Now this test is not intended to torture you (though I know some people might argue with me on this one).
It turns out this is a very important skill once you’re on the job as a management consultant, especially as a first year analyst or associate.
In addition to a live case interview, the McKinsey Problem Solving Test, other firms have used similar tests (Monitor has done this from time to time) OR have given an in-person case interview where the candidate is presented with a written document consisting of various facts, figures and other data… and the data sufficiency skill is tested verbally.
These are all variations of the same thing.
Given a set of data, will you determine the correct, logical, and factually supported conclusion every time?
So bottom line, this skill is pretty important and based on the many emails I’ve been receiving from aspiring consultants around the world, it seems many people are having a difficult time figuring out how to practice these skill.
So just for kicks, I thought I’d give you an actual data sufficiency type question that a McKinsey Partner in the Los Angeles office asked me when I interviewed there for my final round several years ago.
Before I give you the question (which is posted on my blog), I strongly recommend that you read the question and then immediately hit the “post comment” button to post your answer on my blog.
(You can do so with just your first name or initials if you want to be a anonymous)
The key is to post your answer WITHOUT seeing other people’s answers!
(otherwise it sort of defeats the purpose of practicing, and there really are very few opportunities to practice this skill.).
I will be “grading” all the answers posted in a day or two.
Here’s the question:
Volvo recently ran an advertisement that said:
Volvo – The Safest Car in the United States*
* New US government report shows that fewer people die in a Volvo than in any other car brand in America
(Note: A prior version of this blog post indicated that Volvo was the Safest Car in the World. My intention was to write U.S., so some of the answers you see may reflect this.)
Assess the validity of this statement, you have 3 – 5 minutes to do so. You are NOT permitted to ask any clarifying questions. Please be SPECIFIC in your answers. Go!
Click Here to Post Your Response
(Remember: Don’t cheat by looking at everyone else’s response first, look at them AFTER you post your response.)
Scroll down to see the hundreds of answers submitted by readers of my blog.
To see my answer to this question (ideally AFTER you try to answer the question yourself FIRST), click here: McKinsey Problem Solving Test – Example 1 Answers.
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Volvo’s statement is not valid if drawn entirely from the U.S. report because the report deals only in absolute numbers while the statement is a relative comparison to other car brands. The report reads that less people die in a Volvo than in any other car, but that could be because only one person in the country owns a Volvo (the point is exaggerated). The information needed to defend the statement would require data that is adjusted for these variables. Such data would deal in percents of deaths of Volvo drivers compared to other drivers.
In addition, one could also argue that death is not the only criteria for safety. If Volvo’s frequently crash but just aren’t regularly fatal accidents, safety is still an issue.
The claim of “safest car” indicates that the cars are involved in fewer accidents and/or accidents that do happen lead to fewer injuries, when measured on a basis relative to the number of cars on the road. It is not possible to validate the statement without information on how many cars are on the road, and how many are in accidents.
No. The death percentage is more important .
The supporting statement does not offer enough information to assert that Volvo is the safest car in the US. The primary issue is that we can’t speak to the proportion of cars on the road that are Volvos. It might be that Volvos have the fewest fatalities only because they are a small percentage of the cars driven in the U.S. To support this assertion we would need to compare fatalities on a per-automotive basis, though even then we might find that Volvo drivers travel less frequently or on less dangerous roads.
1. Number of deaths isn’t capturing the entire risk: it’s problematic to overlook injuries etc.
2. A more relevant index to look at is :
(number of deaths of drivers of a specific car brand)/(number of cars of that brand on the road). An even better approach would be to use a regression of some sort: It is possible that the low number of deaths is due to the profile Volvo drivers (40-50 years old with families) and not the safety of the car itself
The assumption is “fewer people die in a volvo than in any other car in America”.
Let’s be rational.
- If the “fewer” means that the absolute number of people dying in a volvo is inferior to the absolute data for any car brand in America, it may mean either that Volvos are actually safer, or simply that there is a few less volvos than other car brands in the US (with the same, or even larger #Deaths/#Cars ratio). In this case : I don’t know. Don’t have enough data to relevantly test any hypothesis stated.
- If “fewer” is already based on a #Deaths/#Cars ratio, i.e. given a same number of cars, there are less deaths in volvos than in other brands, the assumption is apparently more accurate.
Even in this case though : That you die less doesn’t mean that you are less injuried than in other cars. To evaluate that I woud rather look for, say, a #(injuries above some level including death)/#accidents and #accidents/#circulating cars ratios for every car brand in America. The safest brand would be the one which is a less likely to lead you to serious injury in a accident, and the one able to prevent you from getting into an accident (with active security, for instance)
First in order to validate this statement you need federal regulated organization’s report.
Either publicly entrusted IIHS or safercar.gov will help validate this report.
Second you need to gather facts about how the car is different.
Test how materials used in manufacturing integrates safety.
For example compare the seatbelt harness to other brands. From my personal experience Volvo does have body friendly harness system.
Third validate traffic accident death report via contacting US police depts to get results.
Latter three processes shall be enough
The fact that fewer people die in a Volvo is a good indicator that Volvo could be the safest car in the US, but this statement cannot be considered completely valid based only on this information.
In order to verify this we need to know what’s the proportion of Volvo cars owners compared to others.
It could be that a very high percentage of Volvo’s owners are crashing and dying, but this number is not big enough because there are only a few Volvo owner’s. So other brands’ cars could be a lot more safer.
For example: let’s say there for each 100 cars in the U.S., 10 are Volvos and 50 are GMs. If 40% of the Volvo’s owners died in a car accident, it would represent only 4 deaths. Bu if 10% of GM’s owners died in car accidents it would represent 5 deaths.
So in absolute numbers, less people died in a Volvo, but relatively, GM’s cars are a lot more safer.
Its fair to say that they have an alright safety record, but the number of volvo cars need to be compared with the number of other cars on the road.
What is the total number of accidents happened?
This statement cannot be supported, becuase we’d need addt’l info to validate it, such as:
% of US cars that are Volvo’s
% of US accident deaths that are Volvo’s
# accidents Volvo’s are involved in per Volvo death, vs. that of all US cars
Average daily driving distance for all US cars / Volvo owners (highway vs. local)
What was sample set of report?
The statement may be statistically true; however, on the flip side of the coin, statistically there may be far fewer Volvo car owners in U.S. Another approach would be to look at the demographics of Volvo owners, and one might find that the majority of owners are middle to older aged people who are more likely responsible drivers than younger generations. This statement does not reference or the physical qualities that the Volvo might have to make is a safer vehicle than others on the road. Overall, the validity of this statement, without further details is weak.
The analysis path to quality this statement need to be around..
1. % car users in US who use Volvo car (to assess whether it represents a fair population)
2. Segment the number of accidents into different categories. Though the accident does result in death, depending on the number of accidental incidentals, associated car and then how the situation prevailed on the spot are the key parameters
3. Though the accident did not result in death, how the safety equipment on board reacted to the accident is the key parameter in assessing / branding a car as Safest
The profile of american who holds a volvo may not be representative of US drivers and does not inform about the safety feature of the car. Taking into account that statistically young male drivers are the most subject to get car accident, I am not sure volvo’s carholders are young male drivers.
The statement is too generic and should specify the category of drivers.
Taking into account that if volvo only represent 1% of US car market, it is statistically evident that accident generated by volvo car holder is among the lowest in comparison with other brands that are much broadly widespread among american drivers.
I think that the main point is that there are few volvo cars used in US. Factors which would weaken the statement could include
-different volvo drivers behavior (they are bought by those concerned about security)
-different attitude towards volvo cars among other drivers
-other factors
I would first note the number of overall drivers of Volvos in the U.S.. If this is much lower than other car brands, this statement is not validated unless the proportion of deaths to vehicle drivers is evaluated.
I’d then consider the number of deaths proportional to the number of accidents across brands. For Volvo to be safer, the number of deaths per ex. 1000 accidents should be lower than other brands. Thus, getting at the actual safety of the car.
Last, I’d want to know more about the Volvo owners themselves. The statement could actually contain reversed causality – it’s Volvo drivers that are safer, not the car. If most Volvo drivers are 40yr old women – less likely to drive recklessly, it may not be the Volvo brand or car is safe, but the drivers have characteristics of safe drivers.
Fewer people die in a Volvo = Volvo the safest car is NOT enough information.
You can have multiple accidents, you will not die, but others outside the Volvo might.
People that can afford a Volvo might systematically have a safer way of behavior.
Volvos might be systematically driven in particular neighborhoods or roads with less accidents.
Fewer people die in V’s cars doesn’t mean that V is the safest car in the world, because there may be more people get injuried in V’s cars.
Volvo – the safest car in the US
see absolute claim
* how many accidents happen in the US annually
* Each car brand in accident, to get %age of accidents by each car brand in US
relative claim
* what is the %age of Volvo share in the market compared to others
* what is the absolute number of Volvos in market?
* what is the US car volume like
safety ratings
* what comprises the safety ratings?
* what features to they focus on?
America might be interpreted as a continent as well, so in this case America is not only the USA but other countries as well. So far this conclusion may be invalid since there is no factual data about the USA itself.
Validity of Volvo being safest care in America. What data are used to compile this claim. Number of accidents in volvos? As compared to same make, model? Are all standards equal? Speed, driver, types of injuries in particular accident. Are confounding variables held constant to standardize measures?
It seems to be a safe car, but the statement doesn’t provide any standard measure through which it was categorized to be a safe car. what are the number of samples taken into the test? What position did Volvo hold during the last time this test was conducted?
I would agree with the validity of the statement because the source it is using is very much credible (US gov).
I think the question is similar to topics in GRE argument. I disagree with this ad for the following points.
1. What’s the data source which could deduce this conclusion of New US government report?
2. If New US government report do a survey to collect data, whether the collection process is scientific?
3. That fewer people die in a Volvo than in any other car band does not mean the Volvo car is safe. Maybe in the United Stats few people drive a Volvo car. So people die in a Volvo is naturally few.
4. Only one factor to judge the security of car is not reasonable.
The news report indicates that the number of deaths for people in a Volvo is less than that for other car brands in the United Ststes. This might be due to several reasons, first if the number of Volvos is small, or if the number of accidents are small, or if the car is actually safe deaths related to number of accidents is little. To assess the validity of this statement, we need to measure the rate of death for passengers in a volvo. In order to do that, we need to have the following information for each brand in the US: the number of volvos, the number of accidents, and the number of deaths.
There are many factors that could be considered in order to assess the validity of the above statement. If we assume that Volvo has a better car design, making sure that parts of the car that could present danger to consumers are adequately mounted to reduce the risk of accidents (the gas tank, for example), that could be an indicator of safety. Also, one could assume that Volvo cars are user-friendly, having good responses to command and easy-to-maneuver technology, which also increases safety. But, Volvo cars are known for the high price and traditional-fashioned models. This means that only a percentage of the population can afford it, namely people with better education and money. Which leads to the conclusion that although the statement can be true, because of the technology precautions, to some degree it is biased because the target market are older people that can buy expensive cars.
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