Reality Check – ComputingSkillSet.com

As an Austrian, I love cakes. Let's be honest, who doesn't love a good piece of cake? But then, cakes usually contain quite a few calories, and so it is justified to think about this aspect of the pleasure, too. For example, the beauty in the following picture contains 10290 kCal for the entire cake (I know that because I made the cake and did the calculation). With 14 slices in the cake, this amounts to, yes, 735 kCal per slice - whoa! Black forest cake, my wife's favorite, made by me (twice a year) Now, if you or I want to know, how many calories a slice of cake contains, we have to actually calculate that somehow most of the time. In particular, if there is no packaging (from which the cake comes) with nutrition information on it, that calculation can be an interesting exercise. Now, since lots of cakes are homemade, calculating cake calories is the way to go. The usual source for such a calculation is the cake recipe, where the ingredients and their amounts are listed. From such a list, we can calculate the total amount of calories in the cake by summing up the ingredient amounts multiplied by the calories-per-amount numbers for each ingredient. The recipe author may actually have done that for us and give us a number of calories per slice or serving right there, in the recipe. But if we do not find nutritional information in the recipe or don't want to do the calculation, we might as well search the web, using a phrase like "how many calories in a slice of cake?". However, the results from such a search can be as misleading as the numbers in a recipe or something we try to calculate ourselves. Now, you might say: Why? And how bad can that actually be? Read on to find out! For this article, I have taken the time to figure out what can go wrong from a calculation point of view (and other points of view)do a bunch of research on the web for various concrete numbers for calorie counts for cakescrunch those numbers for you and extract important things to learn and take away for anyone, counting/keeping track of calories or not, andvisualized everything or put it together nicely so that you have an easy way of understanding what the individual problems are. So keep scrolling along or use the following table of contents to jump to the point that most interests you. Pitfall: Not Knowing Which Possible Errors Hide in Calculated or Given Calories for Cake This is the general pitfall, but it is important to make clear that, and what kinds of, problems arise when stating a calorie count, e.g., per slice of cake. Ask yourself the following questions: What exactly is meant by a slice of cake? Doesn't that depend on what the cake's shape is? Its height and diameter?Given that we know the shape of both cake and typical slices, how many slices do we assume to be in a cake?Even if two slices of cake are the same size, can we be sure that they are of the same weight, too? Or contain the same ingredients?Even if we know the kind of the cake, does that mean that we know the exact ingredients and their amounts? In other words, is there only a single recipe for each kind of cake? You'll probably agree with me on the fact that the answers to these questions are kind of obvious, once you think about them. Still, it is worth keeping that in mind, when looking at the concrete numbers given everywhere. The reason is that for obtaining a good fraction of such numbers, a couple of the points above were just ignored. Pitfall: Stating Calories for a Particular Kind of Cake Without Specifying the Recipe If I told you that a slice or a 4-ounce piece of chocolate cake contains 283.5 kCal (I just made that number up), wouldn't you ask which particular kind of chocolate cake I mean? Yes, you would, because that makes a difference: is it the one sitting in front of you right now in a cafe? Is it for your favorite recipe? So, I did a little investigation on Google Search: I searched for "xyz cake slice calories" for five popular kinds of cakes, and looked for what data about the calorie count I could find. However, I also specifically checked for the presence of a recipe in each case of the results, where you or I could reproduce the given number by doing a calculation ourselves. And here is the result: I went down in the Google SERP (Search Engine Results Pages) until I found 30 numbers for each of these cakes and counted those with a recipe. CakePercentage of Calorie Numbers With Recipe Chocolate cake with frosting33 Cheese cake7 Marble cake13 Fruit cake13 Yellow cake10 So, basically at least two thirds of the calorie numbers I found had no recipe to show where they come from. Interestingly enough, those entries with a recipe are not among the first, say five to ten in the list. So what should we take away from this? People casually searching for "like, how much calories, kinda, are in this kind of cake, per slice, just roughly?" may actually be well served by the search results.If you or I want to know the calorie count in a specific slice of cake sitting right in front of us, just looking at the next best (or even top) search result is pretty much useless. That's true in particular, if we want to know more than just a rough estimate (e.g., we are counting our daily calorie intake for some reason). Pitfall: Not Getting the Weight of the Cake Slice Right or Ignoring the Weight Entirely A slice of black forest cake: 735 kCal, but also 7.6 oz (215 g) This point has an obvious component: If a slice or piece of cake is double the size, it contains twice as many calories. We all understand that. (Still, I have to admit that I myself like to ignore this fact when eating cake. I mean, just look at the picture ... Ahem, back to the analysis ...) What is less obvious is that inside the question "how many calories are in a slice or piece of cake?" there is a hidden question: "how big, or rather, how heavy is this slice of cake?" The weight of a slice of cake is rather easy to determine, and calories are given per weight of ingredient, so that is also rather easy to calculate. Thus, calories per weight of a slice of cake are a very reasonable number to use. Still, we don't always carry scales around, just in case (at least I don't, plus I am lucky enough I don't have to). So it is also helpful to know, how many calories "a slice of cake" will deliver. However, the differences can be remarkable. This is rather obvious again, if there is a slice of cake sitting in front of you or me, but when searching for numbers on the web, it isn't so obvious. In order to make this more apparent, I crunched the numbers I found on the web for "calories in a slice of cake" with regard to the weight of the slice. IF a weight was given at all, that is, which is the case only 37 percent of the time for my data. So here we go: in the following graphic, I have collected and visualized the percentages for five bins of cake-slice weight. The rather light ones, the still light ones, the middle ones, then some heavier ones, and everything above 7.1 oz or 200 g per piece. I collected and compiled these stats from Google searches for five popular kinds of cake. Here, only those where a weight for the slice was given, are used (55 in total). Now, what do we learn from this? I'd like to offer the following observations: Most of the cake slices that people report calorie counts for (in fact close to 93% of my data), are below 5.3 oz (150 g) in weight. Almost two thirds of my data have a reported weight below 3.5 oz (100 g). Now, I might be atypical (as a cake-loving Austrian), but that seems rather light to me for a piece of cake. Remember the picture I showed you above? That piece, as a reminder, weighs 7.6 oz (215 g).In summary, the average reported weight of a slice of cake in this data set is 3.2 oz (90 g), which I am guessing is an underrepresentation of reality. I mean, come on!A lighter slice is easier to put in the "low-calorie" section of foods, if that's what people are trying to do, so beware of statements like "this slice of cake has below 100 kCal!" It might weigh as little as 1.5 oz (43 g). Pitfall: Talking About Calories per Cake Slice Instead of per Weight I touched upon this particular pitfall at the end of the previous section: the weight of a slice of cake is essential to know, if we want to make use of a particular value for the number of calories per slice. Now, as I mentioned, it is certainly intuitive to ask about the calories per slice of cake, but that can lead to rather large errors, as I will demonstrate below. But before we look at the errors in the numbers, let's look at the numbers. Here is a figure analogous to the previous one, but this time, I've collected and crunched the amount of calories per slice of cake for you in nine bins with a width of 100 kCal each: I collected and compiled these stats from Google searches for five popular kinds of cake. Here, those where a calorie count for a slice was given, are used (148 in total). What can we learn from this graphic? Again, I'd like to offer a few observations: A bit more than three quarters of the values in my data for calories per slice of cake are below 400 kCal. The rest of the values go up to beyond 800 kCal per slice.More than two thirds of the calorie values for a slice of cake as found in a web search lie between 100 and 400 kCal.Knowing that there are some rather small (light) and a few rather heavy slices in this data set is not enough to conclude much about what the size of, e.g., a 400-kCal slice of cake might be.The same lack of information comes into play, if we are to estimate, say, how accurate one of these values is for a particular slice of cake sitting in front of you or me. So, how can we make this situation better? Let's look at an analogous graphic, but for the calorie values per 3.5 oz (100 g) of cake. This means, we'll now approach the most reasonable set of numbers in this entire investigation. For the following graphic, I've collected and crunched the amount of calories per weight for you in five bins: three bins with a width of 50 kCal each between 300 and 450 kCal, plus everything below and above that, respectively: I collected and compiled these stats from Google searches for five popular kinds of cake. Here, those where a calorie count per 3.5 oz (100 g) was given, are used (57 in total). My observations, once again: This distribution is narrower than the ones we have seen before, and that is a good thing. The narrow distribution means that the number of calories per weight is quite similar for all sorts of cakes and recipes.As a consequence, we can assume that the large spread in calorie values for a slice of cake is due to a large extent to the weight of the slice. So, can we make a useful statement about the typical amount of calories in a slice of one of our five kinds of cake, based on all this data? Before we attempt this, we need to look at one more kind of statistic in the next section. Pitfall: Relying on a Single Recipe for Calculating Calories Representative for a Particular Kind of Cake A cake is not the same as another, even if it is the same kind. May sound strange, but after all, there are variations in the recipes for a particular kind of cake. Now, we can ask, of course, how large these variations are when it comes to calories per cake slice. Since we have already seen that it is better not to look at calories per slice but at calories per weight, we'll have a look at the latter. The following table shows the average for kCal per 3.5 oz (100 g) for each of the 5 popular kinds of cake that we already studied above. In addition, I computed the standard deviation for each of the data sets, which basically tells us how different the number in each case are: CakeAverage kCal per 3.5 oz (100 g)Standard deviation of kCal per 3.5 oz (100 g) Chocolate cake with frosting36364 Cheese cake35040 Marble cake36332 Fruit cake37694 Yellow cake36539 So what can we learn from this table? A few of my observations: The average values for calories per weight are rather similar among the different kinds of cake.The standard deviations (the variation among the values for a particular kind of cake) are different:Fruit-cake recipes seem to be the most different in terms of calories, while recipes for marble cake are the most consistent.The errors when relying on the average value for calories instead of on the actual recipe are of the order of 10 to 20% and can be even larger. So the particular recipe used for the slice of cake in front of you or me matters for you and me. However, if we want to make a statement about calories in fruit cake or something similar, we need more than one data point. And finally, with the help of all these numbers, we can attempt to get a more reliable answer to the question that underlies this entire discussion: How many calories are in a slice of cake? The average slice of cake contains 328 kCal. For popular kinds of cake, we find the values in the following table: CakeAverage kCal per slice Chocolate cake with frosting359 Cheese cake347 Marble cake352 Fruit cake209 Yellow cake376 To justify these numbers, consider the following: We know what the average amount of calories per weight for our set of cakes is.that this average per weight is pretty similar for our set of cakes, and probably for many kinds of cakes.the distribution of weights and their averages for a slice of the five different cakes from our data set. From these numbers, we are able to compute the average per slice quoted above by multiplying the average for calories per weight by the average for weight per slice, and that gives us, yes, calories per slice. We thus have 364 [kCal/100 g] times 0.9 [100 g/slice] equals 328 [kCal/slice]. Now, try searching for the question above and see what the top of the Google SERP tells you. Interesting, isn't it? Unless they have picked up my answer in the meantime; in that case, like, tadah! Pitfall: Calculating the Size of a Cake Slice as a Part of the Cake Without Specifying How Heavy the Cake is This point may sound strange at first, but there are a couple of cases, where the weight of a slice of cake is defined by a fraction of the entire cake. This would be useful information, but not without knowing how heavy the entire cake is. Ok, I understand that if this appears in a recipe, then we actually know what goes into the cake and can in principle do the calculation. But as a quick way to get the calorie count for a slice of the cake we are looking at, this isn't enough. In terms of the standard number of slices per cake, there is quite a range to be found online. In my data I found numbers from 6 up to 20 slices per cake as given on the page or in the recipe. Keep this in mind, if you rely on this kind of information for finding out, how many calories the slice of cake in front of you holds. Pitfall: Ignoring Real-World Constraints and Situations After all this analysis and all these possible problems in coming up with the perfect number for the slice of cake in front of you or me, there can be other problems that are more related to the real world. Like these: Who cuts the cake into slices and how? Do they do it exactly as suggested by the recipe used? For example, there are 14 cherries on the black-forest cake I mentioned above a couple of times (as you can see in the picture below). If I put 16 cherries there instead of 14, the calorie count per piece goes down by 13% (the idea is to have exactly one cherry per piece, all the same size). If I use only 12 cherries instead of 14, the calorie count goes up by 17%.Are the recipients of each slice asked how large a slice they would like? That depends on the situation, of course. In our family, we usually ask before cutting a slice from a cake. In a restaurant or at a buffet, choosing the size of your slice of cake may not be possible. Overall, there can be various circumstances that change the "standard" slice of cake, but you get the idea. So, overall, having a precise number is a good start, but relying on any particular number for calories per slice of cake is not a good idea. It is better to determine the slice's weight and use that for a quick calculation to get something reliable. Enjoy! A black forest cake containing 10290 kCal in total. Standard number of slices: 14.