Last night, I took my kids out for an American children’s holiday known as Halloween.
Kids (and some ahem… adults) dress up in costume (I was a penguin this year), go door-to-door, saying “Trick or Treat” and get free candy from the neighbors.
My three kids brought back a record 420 pieces of candy. 
In today’s New York Times, I learned that in the weeks leading up to this holiday, Americans purchased $2.7 BILLION dollars in candy.
So here’s my challenge for you.
Assuming all of that candy is consumed by someone in America, estimate the total number of calories represented by $2.7 billion in candy.
Assuming 3,500 calories consumed results in a person gaining 1 lb (0.45 kg) in weight, estimate how many pounds (or kilograms) of weight the American population will gain. Add a comment below to post your entry.
The winner will receive public acknowledgement of their estimation skills, and I will send them a portion of the candy “tax” I collected from my kids.
Yes, we tax our kids for a portion of their candy collection, as mom and dad provide “infrastructure” and “chaperone” services.
It’s a useful lesson in taxation.
(We tax at a 33% tax rate.)
Mostly it is an excuse to reduce the amount of sugar they will otherwise end up consuming.
For my kids, it’s an excuse to get rid of the candy they don’t like anyways.
Good luck and Happy Halloween!
Entries will be accepted for next 72 hours, and only entries posted as comments below will be considered. A winner will be announced next week.
UPDATE as of Friday, November 4TH AT 12PM ET: New entries are welcome, but not eligible to win, as contest has closed.
329 thoughts on “A Sweet Estimation Question”
Question 1: “Estimate the total number of calories represented by $2.7 billion in candy”
Answer 1: 1,440b calories
Question 2: “How many pounds (or kilograms) of weight the American population will gain?”
Answer 2: ~400m lb (or ~180m kg)
As the formula to convert the Question 1 answer into the Question 2 answer is given, I would focus on answering the Question 1 first.
Thus, to estimate the total number of calories represented by $2.7 billion in candy I would need to know Weight of candy purchased and Calories per 100 grams of candy. However, there are different candy types and thus we should consider those types separately. This divides the question into the following three: (1) what are the different candy types, (2) what is the weight of each candy type group and (3) what are the calories in each candy type group. We would then be able to sum all the calories in each candy type group.
(1) Candy types
There are dozens of different types of candies, but the three main types are amongst the most popular that I usually see. Those three types of candies are:
-chocolates (milk chocolate bars, dark chocolate bars, M&M’s etc.)
-biscuits
-jelly beans (incl. marshmallows)
(2) Weight of each candy type group
As it is impossible to know exactly what the consumption of each candy type is, I would assume that it is spread equally according to the cost (e.g. the cost of each group is the same). Then we can estimate that Americans purchased chocolates for $900m ($2.7b / 3), biscuits for another $900m and jelly beans for the remaining $900m.
The price per chocolate bar (100g) varies from $0.5 to $5. I would think that the median is around $1.5, thus I would take it as an average price (which makes $15 per 1kg). This gives us the total weight of chocolates bought: ($900m) / ($15 per 1kg) = 60m kg
The biscuits are usually cheaper than chocolates, the price per biscuit (100g) varies from $0.1 to $2. I would think that the median is around $0.5, thus I would take it as an average price (which makes $5 per 1kg). This gives us the total weight of biscuits bought: ($900m) / ($5 per 1kg) = 180m kg
The price for jelly beans and marshmallows varies from varies from $0.2 to $5 (100g). I would think that the median is around $1, thus I would take it as an average price (which makes $10 per 1kg). This gives us the total weight of jelly beans bought: ($900m) / ($10 per 1kg) = 90m kg
Thus we have got:
-weight of chocolates purchased – 60m kg
-weight of biscuits purchased – 180m kg
-weight of jelly beans purchased – 90m kg
(3) Calories in each candy type group
Now it would be useful to estimate the total amount of calories in each candy group. Let’s take the following estimates for 100 grams of candy
chocolates – 600 calories per 100g (6k calories per 1kg)
biscuits – 450 calories per 100g (4.5k calories per 1kg)
jelly beans – 300 calories per 100g (3k calories per 1kg)
Then we can calculate the amount of calories per each candy type group purchased on Halloween.
Then the chocolates will represent the following amount of calories:
(60m kg) * (6k calories per 1 kg) = 360b calories
Then the biscuits will represent the following amount of calories:
(180m kg) * (4.5k calories per 1 kg) = 810b calories
Then the jelly beans will represent the following amount of calories:
(90m kg) * (3k calories per 1 kg) = 270b calories
Finally, the total number of calories represented by $2.7 billion in candy will be the sum of calories per each group, which is (answer to Question 1):
360b calories 810b calories 270b calories = 1,440b calories
And then, the weight the American population will gain will be (answer to Question 2):
(1,440b calories) / (3,500 calories consumed results in a person gaining 1 lb) = ~400m lb (or ~180m kg)
To check the answer, we can calculate the weight gained per person. Assuming the U.S. population is 320m people, we can calculate that average person gained:
(400m lb) / (320m people) = 1.25 lb (or ~0.6 kg)
The answer looks OK 🙂
AVERAGE CANDY PRICE:
Prices for candy bags (top sellers during this week) may vary between $10 (high-end brands) and $5 (popular), taxes included, for a typical 40 oz bag in large stores (like Walmart etc), thus between c$25 and c$12.5 per oz. Smaller shops sell smaller bags at higher prices, maybe around c$25-30/oz. Halloween featured candies may sell even higher such as 30-35c$/oz. Fancy candies may drive the sales during this period so we can set an average price just below 30c$/oz or around 1c$/g to keep calculations easy.
AVERAGE CALORIES PER CANDY:
Candies are mainly made of sugar which has around 4 cal/g. However they contain also fat which is more intensive in calories, 9 cal/g. Assuming candies are made 80% of sugar and 20% from fatty sources, their weighted calories turn out to be about 5 cal/g.
TOTAL CALORIES SOLD:
Assuming sales are $2.7B, then:
WEIGHT_CANDIES_SOLD = $2.7B/(1c$/g) =2.7*10^11 g = 270,000 ton
TOT_CALORIES_SOLD = 5 cal/g*0.27Gg = 1.35*10^12 cal = 1350 billion calories
TOTAL WEIGHT GAINED:
An interesting metric useful here is the equivalent cost of calories:
CAL_PER_$ = (5 cal/g)/ (1c$/g) = 500 cal/$ (each dollar buys 500 cal)
Given that 3,500 cal correspond to 1 lb, then:
TOTAL_WEIGHT_GAINED = 1.35*10^12 cal/3,500 cal = 386 million lb.
If we monetize this weight:
WEIGHT_PER_$ = 0.14lb/$ (each dollar “buys” 0.14 lb, that is 3$ buy about half a pound)
CONCLUSION:
The US population gains about 386 million lb. However, given that most of the candies are not equally eaten among the population, we can expect kids between 6 and 15 years (about 40 millions, considering an equally distributed population of 320 million people over a life expectancy of 80 years) to gain more weight. Specifically, assuming kids (between 6 and 15) eat twice as much as the rest of the people, it means that:
40M*1.5x 280M*x = 386 M lb, giving x = 1.14 lb.
Therefore kids can gain an average of 1.5x=1.7lb from celebrating Halloween week.
The Americans gain approximately 300 million lbs in body weight.
Here’s my approach:
So it’s all about estimating how many calories per dollar are bought. I did a quick (1 minute) google search and found that a variety of Mars snacks costs 27$ for 205pc, which are on average ~50 cal per piece.
205pc / $27 = 1025 cal / $2.7
I think this is overestimating the issue slightly, as the average Mars snack has more calories than the average snack size but it’s mostly sugar after all…
So, for $ 2.7 billion, the Americans consume 1.025 trillion calories.
1.025 10^12 cal / 3500 cal = X lbs
=> 1.025 10^9 / 3.5 is approximately 0.3 10^9 lbs
Thanks for the little riddle 😉
Taking an ASP of a dollar per candy and an average of 200 calories in each one (from bubble gum to snickers), that would give us a total of 2.7 B candies x 200 calories/candy = 540B calories, around 155 M lbs.
In addition, this weight is not a equally distributed around the population. Taking that kids from age 6 – 17 (the real candy eaters) represent a of the US population a %5 (to make it round) assigned to adults like me who eat their brother’s candies or at halloween parties, we have a total of 155 M lb concentrated in 64 M candy eaters (20% of US population).
This gives an estimate of 2.5 lb of extra weight per candy eater.
Another useful ratio to consider is that each candy eater eats around 42 candies.
To check the consistency of our result, let’s use your kids example: they brought back 420 candies, with a 3 tax, which gives 280 candies divided by 3 (assuming they are okay sharing the same amount). It’s 93 candies each! Double the inital estimation.
There may be some reasonable explanations for this:
1) Kids population () eat way more candy than the adult population considered (%5). We should then weight this sub-groups.
2) ASP of candy could be lower, which makes for more candy per person
3) Your kids set a candy-eating record this year
In conclusion, it would be within reason to set the average weight gained per candy eater in the US in around 2.5 – 5 lbs.
Cheers from Argentina!
The total number of calories represented by $2.7 billion in candy is about 2250 billion calories. The American population will gain approximately 2 lb by consuming these calories. Below is a brief estimation process. Assuming a bag of 150 pieces candies is about $13.5 (I made this specific number for easier calculation below). Based on my knowledge of nutrition facts, a small-medium size candy has 30 calories. So $13.5 can buy about 4500 calories. The total purchase of $2.7 billion can buy about 2250 billion calories (2.7 billion/$13.5*4500). Then let’s round this to 2100 billion total calories. The American population is about 0.3 billion. Taking the info that 3500 calories gain 1 lb, the weight per person gained is approximately 2 lb (2100/0.3/1).
I wanted to try and do this at different levels of accuracy, as everyone seems to .
Assuming that everyone buys those fun-sized bags of sweets that you have in the photo, the average cost per item is about $0.30. Also, I’m assuming (a bit conservatively) that there are about 100 calories in each item. Also to make it easier, I’ll round the number of calories per pound up to 4000.
So, the spend was about $3bn, so approx 10bn sweets were sold. The total number of calories would be about 1000bn, so the total number of additional weight to the American people will be 250million lb; 1.2lb extra per person!
We can be a bit more accurate, I think. I did a quick check of amazon.com prices for some of the candy you have in the photo. The average price per item is about $0.33 (bulk bought fun-size bags). Calorific value was 121 calories per pack. With a spend of $2.7bn, the number of sweets distributed was 8,181,818,182! With this amount of candy, this totals 990,000,000,022 calories, so a total of 282,857,143lb @ 3500 calories per lb. If we take the most recent estimate of the population of the US (Oct 31, 2016, = 324,824,000) , then you get a total of 0.8596lb per person of weight gained… not as crazy anymore!
But we can try to do a bit better than that.
Let’s assume children under 3 wouldn’t take part. Likewise, children over 16 might think that ‘trick-or-treat’-ing is no longer ‘cool’. Doing a little research, the best demographic data for the US is dated mid-2015, with a population of 321,418,820. The data I’ve found is broken down by sex and age in %. The 3-16 demographic contains 17.91% of the US population, totaling 57,566,111 children. So their total weight gain is 4.91lb each…! Let’s also assume that not all of them go out (~20%) and that each child has to give up one-third of their hard earned sweets to one of their parents in ‘parental tax’, then each child will gain approximately 4.12lb – so parental tax also contributes to children being healthy!
(Bit too detailed I know, but just having fun!)
Assuming 100g of candy is about 500 kcal (information is based on a Twix bar, and off the top of my head it sounds about right for all candy). Then about 700g of candy translates into 1 lb of weight gained.
Assuming people bought the candy in bulk, about 10 USD would probably be enough to buy 700g of candy.
Then 2.7 billion dollars translates into 270 million lbs gained, or roughly a little under a pound for each person in the states, assuming at least 85% of the population participated in the holiday more or less equally.
Also, within your family I’m assuming you and your wife took 140 items of candy, leaving a little over 70 pieces for each kid if they shared equally and didn’t discriminate by, say, age. This is roughly 70*30g = 2100g of candy (30g is actually smaller than the Twix bar, but I am assuming 50g would be near the upper limit for a piece of Halloween candy), which is three times the estimated average! So while you had a very successful Halloween and probably made the money you spent on costumes back in candy (as long as you spent less than 150 USD on costumes), it is certainly a good choice to send some of it away!
PS: As an aside, I was curious to see how this plays into the health trend of giving fruit away, and replacing the same amount of candy with apples would have cost a little under 5 times less and reduced weight gain by a factor of 10.
Assumptions/facts from the internet:
1. Each Oz of candy has ~ 130 calories.
2. Each Oz of candy costs $ 0.81.
Therefore, total calories contained in $2.7 billion worth of candies is 2.7 billion/0.81 * 130 ~ 435 billion calories.
# of kids in american population is 75 million.
Since consuming 3500 calories per person results in the person gaining 1 lb, on an average, this Halloween, an average american can be expected to gain,
435,000/(75*3500) ~ 1.66 lbs.
Total cost of Halloween $2,700,000,000
Cost/piece of candy $0.25
Pieces of candy on Halloween 10,800,000,000
Calories per piece 80
Total calories 864,000,000,000
Calories per pound 3500
Total pounds Gained 246,857,143
Given the $2.7 billion spent on candy we simply need to find and apply the ratio of dollars to pounds. Currently $1.00:£0.82, so the American population will gain roughly 2.2 billion pounds.