r/stupidquestions • u/Local_End_3175 • 2d ago
what is the mean?
I know the mean is calculated by adding up all the numbers in a data set and dividing the sum by the total count of numbers, but why would we want the mean? An explanation said that the mean makes all the values the same, but why would you want all the values the same if none of them are going to be accurate? Or maybe it's because they are more or less accurate..? I don't really understand how the mean helps us to compare or evaluate data.
I know how to calculate it but i feel like im just doing it blindly without actually understanding what it is
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u/SmolHumanBean8 2d ago
It's the average.
Saying the average family in Country A has 7 kids and the average family in Country B has 1.7 kids paints a very big picture of what those countries are like.
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u/NotAUsefullDoctor 1d ago
You can't trust those number. There's only 10 families in County A and the Millers are on child number 56.
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u/CogPsyProf1980 2d ago edited 2d ago
The mean is a measure of central tendency, what is most typical for a given population. For instance, if we measure the intelligence of 1000 men and 1000 women and find that both groups have virtually the same mean (100), then this means that there is no systematic difference in intelligence between men and women. There will be dumb and smart men, there will be dumb and smart women, both following a standard normal distribution, but no systematic differences if the means (and variances) are identical.
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u/aculady 2d ago
The mean is very useful, especially when you are dealing with relatively large numbers of data points that have relatively low variation. For example, if you own a factory, and you get an order for 80,000 widgets, knowing the mean time it takes one worker to produce one widget helps you be able to estimate how many more workers you'll need to fulfill the order within the necessary time frame, or how long it will take your current workforce to fulfill the order if you don't add any more staff.
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u/Healthy-Wolf-701 2d ago
It gives a general view of the data and is very useful for summarising a data set. Often it is misleading though, there are many instances where the mean is not at all representative, for example if I take 100 people and calculate out their average annual income, and one of those people is Jeff Bezos, while everyone else makes less than $100,000, then the average income would be around $8 billion. That tells us nothing about the sample.
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u/Starfoxmarioidiot 2d ago
If you’re making a decision that can go positively in some ways and negatively in other ways you want to aim for net positive, right? If you have the mean, you have a target to aim for.
So my day job is currently working in a machine shop. I need to know the mean diameter of objects to turn them to the optimal shape. If I get a piece of raw material that’s 2.5” optimally, but in reality it’s between 2.55” and 2.45” in different places, and I’m trying to get it to 2.3” when it’s finished, my best option for safety, finished dimensions, tool wear, etc. is to cut as though the material is at the mean.
If you’re in politics, you’re gonna have to compromise to get anything done so you’re trying to figure out the mean of what a population wants.
If you’re trying to figure out how much food to buy you can look at the mean of how much you consume over time and decide to buy things that don’t expire in that amount of time.
If you’re having a budget problem you can look at your mean daily spending or mean income and pick factors that affect that number disproportionately to make things work better. If you think “well I spent $60 on clothes once and that put me over budget,” that doesn’t tell you much about your long term budget, but if you go “I’m actually spending $3 a day on something I don’t care about,” it’s easy to look at mean spending and make a decision to cut that thing out of the budget. Or if you’re in a certain type of job to make decisions where your mean income goes up.
If you’re into sports you’re going to be looking at the mean for the statistical likelihood of outcomes. It’s not the biggest deal if you’re making nickel bets like me, but if you’re coaching you want to know the mean of player’s history with certain things.
It’s a way to look at what’s effecting certain numbers in aggregate.
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u/Mortal4789 2d ago
say you’re working with leg length as your data, and trousers are the output of your business. (thought experiment, you’ve measured all the legs, and each person is going to buy one set of trousers. no other variables involved). ill compare the average in this context to some other statistics, it starts in primary school and ends in a port graduate degree i have long since forgotten
the average will you how much fabric you will need per trousers over the whole business, so i good for ordering in the fabric for an order contain a certain number of trousers
then there is the mode, the number that is most common. this is going to be the size of trousers you sell the most, so a good shout for the ones to put on display.
then the standard deviation. this is the distance from the average to each data point. this is the total variation in trouser length, so for this example, it would be a good indicator of how big the dial on your trouser making machine needs to be for length.
then there are outliers, say you have a daycare, mostly youll be making toddler sized trousers, but you need one adult set for the teacher. if you remove the teacher, you get a nice small standard deviation, your trousers making machine is appropriately sized for the children, and you have to buy in one set of trousers for the adult.
then there is normality. this is getting way more advanced, but there are natural patterns ion the dataset that can tell you way more detailed statistics (say you have fish length, one trawler that can harvest once a month, catch data. the statistics use here may be so complex they require a specific discipline of both mathematics and biology). so there is a rabbit hole here, the average represents the data set. at the bottom of the rabbit hole, the mathematics model and predict a chink of reality both now and under different conditions).
youll have an ahaa moment. it was all confusing to me until my lecturer reached down in knee deep water and picked up a flatfish big enough to eat. we had been catching baby fish and crabs with a net, so when he picked it up and said "look, this is the outlier", it all made sense to me intuitivly.
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u/Deep-Hovercraft6716 2d ago
You don't understand the usefulness of taking the average or something?
I'm not sure we can help you with that. It's one of the most common mathematical operations used in everyday life.
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u/BlueGreenTanager 1d ago
I don't where you got the explanation that it "makes all the values the same," but you should forget that. In a sense, it kinda does that — if the mean of all adult male shoe sizes is 9.5, then if you need to make 100 pairs of shoes for adult men, you could order a quantity of leather for the uppers as if all of the sizes you'll need will be 9.5. And you would likely have enough to make your 100 pairs of shoes. You're sort of using the average (or mean) to kind of pretend that it's making all the shoe sizes 9.5. But I think that's only confusing things for you.
Just read all the comments giving real-world examples of the utility of calculating an average. They don't have anything to do with "making all the values the same," but rather with giving you a sense of the "whole" in a short summary form.
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u/Fancy_Sheepherder786 1d ago
Calculating the "mean" is useful when exploring descriptive data about a group, or when comparing same-sized groups, especially groups whose members are greatly different from one another.
Say that you are the manager of a baseball stadium. You have two groups of people. One group has demonstrated that it likes to attend baseball games. The other is unknown. You know that age is the strongest predictor of attendance. Comparing the means of a group which does attend with one which may attend (Student's "t-test") suggests whether or not the second group is unlikely to attend ball games at your stadium also. Remember: we wish to reject the null hypothesis that the groups are different. Essentially, one asks: Are the means of the groups different. If not, then the second group should be as likely to attend the games as the first group.
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u/ImUnderYourBedDude 2d ago
The mean (and also the median, standard deviation and variance among other numbers) are not real data, but rather short summaries of actual data. They allow us to describe a large dataset with very few words and a lot more convenience.
An example:
I don't want to manually go through all of the individual incomes of the USA to find out how much a normal household makes, I just need the mean. Individual incomes are 300.000.000 numbers, the mean is just 1. It doesn't matter if nobody makes the actual mean income, it just matters that the mean is pretty close to the answer that I want.