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”
Thank you for this brain exercise, and my answer is as follows.
To find the number of calories represented by 2.7 billion in candy, we must first figure out what kinds of candy Americans spend their money on and how many calories are in those candies.
According to National Confectioners Association, 72 percent of candy spent on Halloween is chocolate. Thus, since the vast majority of candy is chocolate, let’s assume that the average candy is chocolate for our calculations.
Now we have to figure out the cost of an average chocolate bar and how many calories it represents.
Research conducted by the Chicago firm IRI in 2013 shows which chocolate brands are most popular in the US. Their ranking of the top 10 chocolate brands uses data of candy bars weighing 3.5oz or less (the size of standard size American candy bars). Although snack size candy bars are often given at Halloween, I was not able to get sufficient data in that category for any meaningful analysis.
From this, lets assume that each unit of candy bar (according to their study) is 3.5 oz, or 100grams. The top 5 popular candies are Reese’s, M&Ms, Snickers, Hershey’s and Kitkat). The average cost of 3.5oz / 100 grams is $1.134 (arithmetic average of the average price per unit)
Thus, dividing the 2.7 billion by the average 100g unit price, we get 2.38 billion units, or 238 billion grams of candy.
Next, lets calculate the average calories in 100grams of candy. For this, a good approximate is an equally weighted average of 100grams of the top 5 popular candies (Reese’s, M&Ms, Snickers, Hershey’s and KitKat).
Reese’s: 515 cal
M&M: 512 cal
Snickers 477 cal
Hershey’s 532 cal
Kitkat: 520cal
Average: around 510 cal
Thus, the total number of calories is 2.38 billion units (100g) * 510 Cal / 100 grams, which equals 1237.6 billion calories. This many calories translates to a total of 0.3536 billion or 353.6 million pounds gained by the American population this Halloween.
Yikes!
Objective 1: estimate total calories (units = kcal) of $2.7 billion in candy
Answer 1: around $1.49 trillion calories
Objective 2: estimate total # of pounds (lbs) f weight American population will gain
Answer 2: around $426 million lbs of weight; in other words, 1.3 pounds in average weight gain per American
Framework & key calculations for objective 1:
Total calories = (Pieces of candy) * (Calories (kcal) per piece of candy) [Assuming all candy is consumed as calories] = (Total cost of candy/Average cost of 1 piece of “fun size” candy”) * (Average calories per “fun size candy) = ($2.7 Billion/$0.16) * (88.3 calories) = 1.49 trillion calories
[Assumption: all candy given out was “fun size,” $2.7 Billion total cost of Halloween candy is pre-tax]
See “support calculations for objective 1” for more details.
Framework & key calculations for objective 2:
Total pounds of gain by Americans, before exercise= (Total calories gainable) * (1 lb weight gain/3500 calories) * (100% gained by Americans) = (1.49 trillion calories)*(1 lb/3500 calories) *100% gain = 426 million pounds of total weight gained by Americans
Average US weight gain = (Total pounds of gain by Americans)/(Estimated US population as of October 31, 2016) = (426 million pounds/325 million people) = 1.3 pounds in average weight gain per American
[Assumption: all candy is consumed by American population, 3500 calories/lb weight gain, no other sources for weight gain | Source: Census Population Clock]
Potential reasons for variance from estimation:
1) A big portion of all candy purchased is never eaten (source: personal experience growing up in the Midwest)
2) Sample of 3 candies and respective quantity-price combos may not be representative of all candy purchased
Support calculations for objective 1:
A1. Total cost of Halloween candy = $2.7 Billion
[Source: question description above | Assumption for B & C: average cost & calorie information of 3 most popular candies consumed around Halloween – Butterfinger, Kit Kat, Reese’s Cup – are representative of all candies consumed in US around Halloween time | Basis for assumption: Influenster poll of 40,000 Americans]
B1. Average cost of 1 piece of “fun size” candy = (Butterfinger estimated cost Kit Kat estimated cost Reese’s Cup estimated cost)/3
= ($0.16 $0.13 $0.19)/3 = $0.16
B2. Estimated cost per “fun size” = Cost per container of “fun size” candy* Grams per “fun size candy/grams per container of “fun size” candy
[Source: manufacturers’ online nutritional information, Walmart website pricing information | Assumption: Walmart candy price selected is roughly representative of candy purchased for Halloween]
C1. Average calories = (Butterfinger fun-size candy calories Kit Kat fun-size candy calories Reese’s PB Cup -size candy calories)/3
= (85 70 110)/3 = 88.3 calories
$2.7 B could buy 2.7/1.14($ per candy on average in the US) = 2.368 B pieces of candy
1 piece of candy ~ 535 Cal
2.358*535 =1267.11 Cal
1267.11/3500 ~
0.362 Billion of pounds weights gained in the US
The total gain is 3billion pounds
1.94T calories
555M lbs
1 treat size (fun size) Calories
Peppermint Pattie 47
Kit Kat 73
Dots 70
Skittles 80
67.5 Average Calories per candy
$2,700,000,000.00 Total Sales
$0.27 per ounce
0.336842105 Ounces per candy
10,000,000,000.00 total ounces
29,687,500,000.00 Total pieces of candy
2,003,906,250,000.00
572,544,642 LBS for the entire population
Total pounds added by the US population = 100 Million Pounds
(Each person is adding 1/3 lb, assuming 300 million candy consuming population and uniform distribution of consumption)
Calculation:
Total spend = $2.7 B (given information)
Each candy cost = $0.27 (assumption)
Number of candies sold =Total Spend / cost per candy = $2.7 B / $0.27 = 10 billion
Calories per candy = 35 (assumption)
Total Calories consumed = Total candies sold x Calories per candy = 10 billion candies x 35 calories per candy = 350 billion calories
Number of calories to add a pound in weight = 3500 (given information)
Total number of pounds added = Calories consumed / calories required to add a pound in weight = 350 billion calories / 3500 per lbs = 100 million lbs
Assuming 300 million candy consuming population and uniform distribution of consumption, each person added 1/3 lbs by eating 30 candies.
To estimate the amount of calories in $2.7 billion in candy, my assumptions are as follows:
1) A consumer could acquire 50 grams of candy for $1
2) On average, a piece of candy is made up of 30% fat and 70% sugar. A very small amount of the latter percentage would actually be protein, which contains the same amount of calories as sugar, so calculation-wise, this does not matter now.
3) A gram of sugar contains 4 kcal, a gram of fat contains 9 kcal.
First, we need to know how many grams of candy $2.7 billion would buy:
$2.7 billion x 50 = 135 billion grams.
Next, we need to know how many calories are in those 135 billion grams of candy. That would be:
135 billion x 0.7 x 4 = 378 billion kcal from sugar (and some protein).
135 billion x 0.3 x 9 = approximately 360 billion kcal from fat.
This totals to a whopping 360 billion 378 billion = 738 billion kcal.
Assuming a person would gain 1 lb for every 3500 kcal consumed, this would mean a total of 738 billion / 3500 = approximately 210 million lbs gained.
Let’s assume there live approximately 300 million people in the USA. And that about 25% of those people are below the age of 18.
That would be 300 million / 4 = 75 million children.
I assume about 70% of the US population celebrates Halloween (I do not live in the USA, so I do not know how viable this is).
This would be 75 million x 0.70 = 52.5 million children partaking in Halloween.
That would be 210 million lbs / 52.2 million children = approximately 4 lbs gained per child.
To check my numbers (and for added fun), I will apply them to the data you provided:
Let’s assume each piece of candy is approximately 20 grams. Your children brought in 420 pieces of candy, that would be:
420 x 20 = 8400 grams of candy. Based on the assumptions about calories I made earlier, this would be:
8400 x 0.70 x 4 = approximately 23500 kcal from sugar, and
8400 x 0.30 x 9 = approximately 22700 kcal from fat.
This would make a total of 46200 kcal, or 46200/3500 = 13.2 lbs gained. This would mean you would have 13.2lbs / 4 lbs (from my earlier estimation) = 3.3, that you have about 3 children, which, I believe, is the case. Based on these numbers, I would say my estimation seems pretty reasonable.
By the way, since you were kind enough to tax some of your kids’ income, this would mean you would gain about 4 lbs from all that candy. Clever of you to share this ‘heavy burden’ with someone! I hope you’ll enjoy it! 🙂
A fun-size candy, usually purchased for Halloween (I am taking Snickers as the benchmark), weighs about 34g, costs around $0.16 and has 80 calories.
So that would lead to about 1,667,6199,895 fun size candies.
The calories from these would lead to a collective weight gain of 381,170,283 pounds for those celebrating the festival.
Andddd if we see the numbers and have about 40 million people in US going trick or treating, that’s a weight gain of approximately 10 pounds per person! Feeling tricked with the treats, eh?
Assume:
– 1kg candy = 5k calories
– 1kg candy = $5
– US population = 320 million pers
Work:
$1 = 1k calories
$2.7 billion = 2.7 trillion calories (total)
3.5k calories = 1 lb
2.7 trillion calories / 3.5k calories = 0.77 billion lb (total, i.e. US population) = 770 million lb
Bonus:
770 million lb / 320 million pers = 2.4 lb / pers = 1.1 kg / pers