Estimation Problem – Sample 'Correct' Answer
Note: the solution below is an example of the format I expect for your answers to estimation
problems – but you should not just cut and paste my answer and edit it with your work.
Question: Estimate how many televisions there are in the United States.
Note: Please do each part below honestly, without looking ahead. This is how you become
proficient at such problems, and 'cheating' by finding the answer ahead of time will only hurt
your ability to improve. Remember that I care much more about your 'process' than I do about
your answer.
a.
Please follow a type of process similar to what we have done in class to make your
estimate. Use only 'single estimates' rather than 'ranges' - i.e. use midpoint guesses
along the way.
Answer: We can estimate the number of TVs in the US by considering a segmentation of the
total population by household type and adding up the results. We assume that the vast majority
of televisions are in households, although of course there are many in businesses, etc. (As you
will see below, this ends up being a fair assumption given that our real data source is TVs in
homes to act as a comparison).
Assumptions:
 There are about 100 million households in the US
Of these households (100 million, thus any million subset is also an equivalent percentage)
assume that:
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20% are for single people
20% are for married couples beyond retirement age
20% are for married couples without children
40% are for married couples with children

Assume that single person households have 1 TV set (because they only need one TV and
can use it in whatever room they want).
Assume retired couples have on average 1.25 TV sets. This is because they previously
had kids that watched TV in their own rooms, etc.
Assume that married couples with no children have 1.5 TV sets (because both were
previously single and when they got married they didn’t always both bring their TVs).
Assume for married couples, depending on number of children.. (This is based on the fact
that each kid doesn’t necessarily have their own TV set, but may share it in a room with a
brother, sister):
o 30% have 1 kid and 2 total TV sets
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o 50% have 2 kids: 2.5 TV sets
o 20% 3+ kids: 3 sets
So the total number of TVs = 100 million*(0.2*1 + 0.2*1.25 + 0.2*1.5 +
(0.4*(0.3*2+0.5*2.5+0.2*3))) = 100 million*(0.2+0.25+0.3+0.4*(0.6+1.25+0.6)) = 100
million*(0.75+0.4*(2.45)) = 100 M*(0.98+0.75) = 173 million
b.
Compare your answer with 'real data'. How close were you to the answer and
comment on the 'difference' between your estimate and the real data, specifically on
how your choices of assumptions might have led to the difference.
From the 2002 Statistical Abstract of the United States (Table 1103, p. 699), there were 245
million TVs as of the year 2000. Over the period 1994-2000, about 5 million more TVs were
added per year. Thus there are probably 260 million as of 2003. Regardless, our estimate above
is about 35% lower. In short, while were in the correct order of magnitude, our answer was way
off.
The same Table 1103 referenced above notes that the average number of TVs per household is
about 2.4. While we did not specifically find an average per household, our number above was
1.7 per household – accounting for most of the difference in our estimate and the actual answer.
Americans have lots of TV sets!! Thus given this information, we at least need to make sure
our per-household estimates are generally higher.
Given the way we segmented the households above, there are certain categories that led more to
the error than others. For example, the estimates of single and retired households (about 1 TV
each) are probably pretty good estimates. Thus, the married couples are what should be better
estimated.
c.
Use a more robust analysis (either on paper or via Excel) to make your 'original
model' better. Use ranges of assumptions, more robust assumptions, etc.
As mentioned above, the focus of this estimate will focus on the married couples, although we
will use ranges for all of the segments. Using the same general assumptions as above, we now
use the following segment assumptions (note that for simplicity I have not made a range for
number of households, but this would be another good candidate assumption for a range):


Assume that single person households have 0.75-1 TV sets (because they only need one
TV and can use it in whatever room they want).
Assume retired couples have on average 1-2 TV sets. This is because they previously
had kids that watched TV in their own rooms, etc.


Assume that married couples with no children have 1.25-2 TV sets (because both were
previously single and when they got married they didn’t always both bring their TVs).
Assume for married couples, depending on number of children (This is based on the fact
that each kid doesn’t necessarily have their own TV set, but may share it in a room with a
brother, sister):
o 30% have 1 kid and 1.5-3 total TV sets
o 50% have 2 kids: 2-4 TV sets
o 20% 3+ kids: 2-5 sets
So the low end estimated number of TVs = 100 million*(0.2*0.75 + 0.2*1 + 0.2*1.25 +
(0.4*(0.3*1.5+0.5*2 + 0.2*2))) = 100 million*(0.15+0.2+0.25+0.4*(0.45+1+0.4)) = 100
million*(0.6+0.4*(1.85)) = 100 M*(0.6+0.74) = 134 million
So the total number of TVs = 100 million*(0.2*1 + 0.2*2 + 0.2*2 + (0.4*(0.3*3+0.5*4+0.2*5)))
= 100 million*(0.2+0.4+0.4+0.4*(0.9+2+1)) = 100 million*(1+0.4*3.9) = 100 M*(1+1.56) =
256 million
Even with this better analysis, our high end estimate is just barely at the level of the 'real data'
found above. Its surprising given our assumptions above already have many TVs per household.