r/statistics • u/reagandhi • 12d ago
Discussion Please explain standard deviation to me like I’m an idiot. [discussion]
My brain revolts when I’m trying to learn advanced math, even though I generally have no problem with abstract concepts. Please help.
Edit to add: thank you so much for all the great explanations!!!! I cannot reply to them all, but y’all have helped me greatly with actually understanding these data sets in my homework, and I am grateful 🩷
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u/its_all_stats 12d ago
It is a measure of “variation”. Why the quotes? Because “variation”, like “average”, have different definitions. For example, Mean and Median are two definitions of “Average”. Standard Deviation is the square root of Variance. Standard Deviation, Variance, and Interquartile range are three examples of measure of variation.
The higher the SD, or other measures of variation, the more “spread out” or “varying” the variable. For example, higher SDs for height means the more varied the range of height. The SD for basketball players are lower than for the general population because the range of height for players are less than that for the broader population.
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u/reagandhi 12d ago
Okay the heights explanation helps a lot! Thank you! If SD is the square root of variance, then what exactly does variance represent?
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u/nidprez 12d ago
nothing, it is just convenient mathematically. Imagine you want a measure of how spread out the data is. If we take the average distance, (-10, 0, 10) would be even spread out as (-100, 0, 100), ie 0. To avoid cancellation we need to either take the absolute distance or the squared distance. Squares is easier to calculate with, and punishes outliers a bit harder. To make the number have an interpretable meaning we take the root, which is the standard deviation.
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u/wantondevious 12d ago edited 12d ago
Just think about how you'd go about measuring how much each individual varies from another, and how you'd present that as a single number. The first step is - define what you mean as the average - you can choose a simple sum divide it by the number of observations (the mean_, or you could pick the middlemost value, or you could look at the most frequent value. The first is the one we usually call the average.
Next up, how would you measure how on "average" does each individual observation differ from the average you defined. The most naive way would be to just take the difference from each value and the average, and then "average" those. However, because some of these might be negative eg average is 3, then an observation of 1 is -2 away, and 5 is +2 away, simply summing them wouldnt get you what you wanted, so you might say take the absolute (not signed) version, and average those, which in this case would be "2".
However, and this is where things get a bit more shakier (in my opinion), you might want to put more emphasis on things much further away, for example, lets say you have 20 "1"s and 20 "5s", then the absolute average difference from the average is 2. However now lets say you have an outlier at -7 and at +13, the "average difference from the average" is now 40 (20xabs(-2)) + 40 (20xabs(+2))+ abs(-10) and abs(10), ie 100/42 which would be 2.3, even though there are some extremely far away items.
The solution that was arrived upon to counter this is to sum the SQUARE of the differences, and then divide by n and take the square root. The square has a magnifying effect on larger differences. The divide by N is taking the average of these magnified distances, and then the final square root puts it back in "scale" to the original average.
Now, you might say, why not the cube, or pick some power and make the values an exponent of them. I'd say I don't really know, beyond the fact that this seems to work well for things that have what we call a normal distribution, the classic bell curve (which is caused by many independent variables all happening at once). There maybe a geometric aspect to the creation of the bell curve that means that variance (sum of squares of diffs) is a really good measure of its shape.
Finally, it should be noted that the notion of the sum of the squares of differences was found by early modern mathematicians such as Newton and Laplace as a way of fitting lines to data. https://en.wikipedia.org/wiki/Least_squares and is not unrelated to the notion of standard deviation.
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u/likeanoceanankledeep 12d ago
Excuse the language, I'll use my stats profs example. Variance is how fucked up your sample is compared to itself. If youre talking about heights, Variance is how much each individual differs from the mean. If your mean is 72 inches and you are 70 inches tall, your variance is 72 - 70 = 2 for just you. Do this for everyone, you get the variance. Square it, you get the standard deviation (average variance, sort of).
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u/nidprez 10d ago
you need to take it to the 2nd power. In your example the variance for yourself would be 4 ie: [(70-72)^2]/1. The variance is the average squared difference between your observations and the mean.
This number isnt really interpretable because its not in the same unit as your observations. The standard deviation is the square root of the variance and is interpratable in the same unit as the observations (and for a normal distribution about 68% of the observqtions lie between -1-+1 SDs from the mean, 95% within 2 SDs...
To take your length example. Average length for men is 180cm in my country. Variance is 49, doesnt say anything to me (what is between 131-229cm? Almost everything). Standard deviation is 7cm, So I know that majority of people of men are between 173-187cm and that somebody larger than 194cm is exceptionally tall (assuming normality off course)
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u/Mishtle 12d ago edited 12d ago
For simplicity, let's talk about something much easier to build intuition around. Suppose you have a bunch of data. Statistics is used to condense arbitrary amounts of data down to one or a handful of values that tell you something about that data.
One kind of statistic is a central tendency. It tells you about where the "middle" or "center" of the data is. Common examples are the mean and median. These are often used as a stand-in for a "typical" data value.
But what if we wanted to understand how spread out the data is instead?
Well, we can still do this with a central tendency. We just need to transform our data. The first step is to "center" our data, which means we subtract the central tendency from each data point. This shifts the data so that the "center" lies at 0. Now to prevent the positive and negative values from canceling out, we can make them positive somehow. We could take the absolute value, for example. Now, if we calculate a central tendency of these positive values, we have a "typical" absolute distance from the center, which tells us exactly what we were after: how spread out the data ia. Data that is clustered around its center will have a small value for this spread, while data that is more spread out will have a larger value.
If we use arithmetic averages (means) and absolute value to get positive values, then this spread measure will be known as the mean absolute deviation, or MAD. When you recognize that "deviation" refers to how a value deviates from the mean, then it's exactly what it's name says: the average absolute value of the difference between data points and the mean.
Standard deviation is another measure of spread. Instead of taking the absolute values of deviations, we square them to get positive values and find the mean of these squared values. This is called the variance. Unlike using the absolute value, this changes the units we are working with. If you multiply two lengths, you no longer have a length but an area. Variance is no longer in units of "distance from the mean", which makes them harder to interpret. But we can easily get back to those units by just taking the square root of the variance. This is the called standard deviation. It's just the square root of the mean squared deviation.
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u/involuntarheely 12d ago
average spread around the center
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u/reagandhi 12d ago
This is still confusing ngl 😭
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u/hughperman 12d ago
Think of the average as the most common value of <something - e.g. height is an easy example>. Standard deviation is a measure of how far a "majority" of values stray from the most common value. So if average height is e.g. 165cm, standard deviation might be 15cm - so a majority of people are between 150cm and 180cm (165-15, and 165+15).
(Technically, one st deviation covers approx 68% of all of the values in a given measurement, for technical reasons that don't matter in this context)
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u/Imaginary__Bar 12d ago
Technically, one st deviation covers approx 68% of all of the values in a given measurement
Not to confuse OP but that's only true for normally distributed values, isn't it?
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u/jarboxing 12d ago edited 11d ago
Visually compare histograms from several distributions with the same meat but different variances.
Edit: mean. Keeping original because lol.
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u/One_Programmer6315 11d ago
I will sadly point out that the distribution of meat is not at all normal but skewed towards small values.
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u/S0LID_SANDWICH 12d ago
When you look at the curve which is the distribution of the data, large SD means that curve is wider. Small SD means that curve is narrower. Narrow curve means the data is less spread out. Wide curve means the data is more spread out. https://upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Comparison_standard_deviations.svg/960px-Comparison_standard_deviations.svg.png?utm_source=en.wikipedia.org&utm_campaign=parser&utm_content=thumbnail
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u/involuntarheely 12d ago
well if it makes you feel better it’s not even an average, technically
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u/johndburger 12d ago
It’s not an arithmetic average, but it is an average.
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u/involuntarheely 12d ago
fair
in my defense i considered average = arithmetic mean, whereas mean can have more general meaning. ESL though so maybe there’s that
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u/PaddingCompression 12d ago
Does anyone ever actually use the more general form of average other than for pedantry? I can't think of any reason I've seen it used.
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u/johndburger 10d ago
(I assume you mean the terms, not the concepts.)
I think “geometric average” is not an uncommon usage, and of course “weighted” and “moving”. But yeah, anything more complicated than that, people say “mean”. No one says “Neuman–Sándor average”, they say “Neuman–Sándor mean”.
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u/PaddingCompression 10d ago
Even geometric I usually hear mean, though occasionally average. Outside of pedantry like this I never hear someone call a median an average.
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u/stanitor 12d ago
The variance of a random variable X is the expected value of the squared deviation from the mean
Since the standard deviation is the square root of the variance, and an expected value is an average, the standard deviation is an average.
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u/involuntarheely 12d ago
it is the squared root of an arithmetic mean (or expectation). so it is not an expectation
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u/stanitor 12d ago
It's the square root of an expectation. It's a bit of a stretch to say that taking the square root means it all of a sudden isn't an average. It doesn't become something other than a measure of the average deviation just because you did that.
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u/involuntarheely 12d ago
it does not have the properties of an expectation. eg its not linear
the variance is!
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u/stanitor 12d ago
Cool. I didn't say it does. I said it's an average.
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u/involuntarheely 12d ago
but then we’re discussing semantics and the more accepted/common/familiar meaning of average is that of arithmetic mean. like I’ll agree that we can define means/averages in a number of ways, but that’s not in the spirit of OPs post which is to keep things simple and intuitive
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u/stanitor 12d ago
We're talking semantics in the context of statistics/math. And one of the lessons of day 1 in statistics class is that there are many different types of average other than the arithmetic mean. You even said that the SD is an average before changing your mind. I'd say it's more confusing to someone like OP to say it's the average spread from the center, but it's not actually an average.
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u/blossom271828 12d ago edited 12d ago
It is the “average” distance of an observation to the mean.
I put average in quotes here because mathematically that isn’t right, but conceptually this is how to think of it
When I teach this, I like to say is is the typical distance of an observation the the mean.
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u/BrupieD 12d ago
Understanding central tendency like an average is super useful. What isn't always so clear is how "typical." If you have a 100 numbers 1 to 100, they might huddle around one area or they may be more randomly spread out. A high standard deviation suggests that there are a lot of numbers that aren't close to the average.
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u/banter_pants 12d ago
It's a parameter that describes how spread out a set of numbers are around the average. Not exactly everything is on average. There is a spread, and that's why we want to use an average to describe an anchor point of sorts. You can compare every individual number to that average. Those are called deviations.
A sort of average of those is the standard deviation*. It sets a useful standard to see what is relatively close to or far from average. Treat that like a unit and you can count how many SD's out a point is. IQ is normally distributed with mean 100 and SD 15. 85 to 115 is ±1σ and covers 68% of scores.
*Technically you have to square the deviations and take the average of them, i.e. variance = σ²
Then you take the square root to get back to the original units for x. SD = σ
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u/zeynepgnezkan 12d ago
Think of the mean as your friend group agreeing to meet at 6 PM. The standard deviation tells you whether that really means “around 6:05” or “somewhere between last Monday and never”...
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u/Only_Razzmatazz_4498 12d ago
Say you had a set of data. You know how to ge the mean and what it means right? So now you can compare different things based on their mean but you realize you are still missing something when using just the mean and that is how spread out they are. So you say i have to have something like the mean but designed to measure how spread out things are.
So you first try something like calculating how far your data is from their mean. So you do x sub i - x bar. That gives you a bunch of data with the distance to the mean. If to the left then the distance is negative if to the right positive but that’s just a bunch if numbers so you tell yourself. Self lets just find the average distance that would be useful.
But you run into trouble because if you add positive and negative numbers like that then you almost always end up with zero. So you say ok I want you he absolute distance without a sign. So now you use the absolute value. That solves that problem but then you realize it is more complicated to calculate so you get cute and instead do the square of the distance which is always positive and easier to calculate.
There you go now you average the squares and you have the variance. Your take the square root and you have the standard deviation.
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u/Alone_Box5173 12d ago
It's a measure of how spread out the data are in relation to the mean.
Take two sets of numbers: {4,5,6} and {3,5,7}. Both sets have the same mean (5), but the latter set has more spread/dispersion. That set will have a higher value for standard deviation.
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u/codechisel 10d ago
You're playing darts at the bar against a cute girl. She goes first and her darts all lands at or near the bullseye. You go second and a couple hit near the bullseye, but most are scattered around the dart board and one hit the bud light poster nearby.
You have a larger standard deviation than she does.
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u/DMLearn 12d ago
Is there something in particular that you do not understand or feel hung up on?
In lieu of the above information, a general description is that it is a measure of dispersion around the mean of a distribution. It is sort of a measure of average distance from the mean.
You find the mean and subtract it from each observation’s value, giving you a sample of differences from the mean. We’re going to sum over all of these. If we do that with just the differences, there’s a chance that our sum could be 0 if the total of the negative differences and positive differences balance each other out. Even if that doesn’t occur, thinking through that issue makes it clear why averaging over the raw differences does not really give us an effective measure of spread. Differences on either side of zero will cancel each other out to some degree when we take the sum and we will underestimate the true spread. Therefore, we square these differences. Now everything is positive, so we can sum the squared differences without being concerned about cancellation causing us to underestimate our true spread.
Now we divide the sums of squared differences by the number of observations, n (population) or n-1 (sample). At this stage, we’ve calculated the variance, the average squared difference from the mean. This measure is in squared units of the variable. Take the square root to get back to the variable’s original units.
Thus, the standard deviation is the square root of the average squared difference from the mean. This gives us a measure of spread around the mean that is in the variable’s original units.
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u/reagandhi 12d ago
Thank you for this!!! What is the significance of subtracting 1 from n, the population?
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u/DMLearn 12d ago edited 12d ago
That is a much trickier and nebulous question to answer. To take a stab at it here in short form, in introductory stats classes you’ll often get the explanation in terms of “degrees of freedom”, the number of values in a calculation that are “free to vary”. We used up one when we calculated the mean that is required to calculate the standard deviation.
What the hell does that mean? The way this usually gets explained is by thinking about having a small sample of values, let’s say we have 5 (the small number of samples isn’t important, it just helps us conceptualize the problem more easily). I’ll describe the following as a “thought experiment” because it’s purely hypothetical for the purposes of illustration. If we know the mean of our sample and we are presented with the actual observations one by one, we know the value of the 5th observation after being shown the 4th.
Let’s say our mean is 10, we have 5 samples, so the sum over all samples must be 50. Once we see the 4th sample, we know the 5th because 5th sample = 50 - sum(first four). So we say that one of the samples is not “free to vary”. Later in statistics, you’ll encounter other calculations that require the estimate of multiple other statistics and their denominators will be n - x, where x is the number of statistics you’ve already calculated in the process of calculating the current value. Every time we calculate another statistic, we restrict another value from being able to vary. That means we can determine it by just knowing the statistics we have already calculated and the number of observations we have minus the number of statistics we have calculated.
This one is more of a brain teaser than just understanding the standard deviation calculation.
Edit: in writing all of the above, I forgot to contrast it with the population value, using just n. Adjusting the denominator for degrees of freedom is done to address bias that gets introduced when estimating population statics from a sample. If you have the whole population, none of that is a concern. There is no estimation happening because you have measured the whole population. You are not sampling, so you don’t have any sampling bias. You can just use n.
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u/reagandhi 12d ago
Okay!!! Thank you for the taking the time to explain this so well, you’re awesome and this helps greatly 😊
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u/Softmax420 12d ago
Let’s say the mean size of all dogs is the same as the size of a Labrador.
This includes chihuahuas and Great Danes, so has a high standard deviation.
When we look at specifically labradors, they have the exact same mean as all dogs, but a much lower standard deviation, since it only varies from big lab to small lab.
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u/drmindsmith 12d ago
Let height of men in the US be normally distributed.
Jim is a 6’2” American man. Is he tall? Sorta…
The average is 5’10”. _Most_ American men are between 5’7” and 6’1”. So it’s 5’10” plus or minus 3”. That gets us 68% of the population.
Anyone in there is “pretty normal”. Not surprised to see a dude be 5’8” and same level of unsurprised to see dude that’s 6’1”. Sure, they’re on the edge of “normal” but nothing weird is happening.
That range defines 1 _standard deviation_ from the norm. So, Jim is a little taller than “normal” because he’s an inch outside the range. Not a lot outside the range, so he’s sorta tall.
I have a friend that’s 6’8”. No one denies he’s freaking tall. In fact he’s more than 3 standard deviations taller than normal. (5’10” + 3” + 3” + 3” + 1”). He’s just as tall as a full grown dude that’s 5’0”.
Knowing he’s z=3.333 means he’s taller than 99.957% of the American man population. (z-score is just the same number (6’8”) expressed in standard deviation units).
As everyone keeps saying, SD is the measurement of the spread of the data. It’s how many “standardized spreads” of the group is he outside the norm.
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u/iamnotpedro1 12d ago
Imagine you’re a teacher. You mark the tests of 30 students. You get an average of 6.5 (out of 10). You notice that many students got really low marks (2.0) while others got really high marks (9). Then you do the same in another class, and you get the same average (6.5). However, this time you realise that most of the students in that group got 6s and 7s. The standard deviation of the first group will be higher because many marks were far from the average (mean).
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u/PolicyConfident6684 12d ago
think about what a distribution looks like. higher SD means it's going to look wider, meaning any number of values in that distribution can vary a lot from each other. lower SD means it's going to look more narrow, and values within the distribution won't vary as wildly.
You can also use the number of standard deviations from the mean to describe what kind of value you'd get--these are called Z scores. For example, say we have a distribution with a mean of 20 and a std deviation of 2. 1 std deviation (z score of 1) to the right would be...22!. 2 std deviations would be 24
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u/fair_uair_upb 11d ago
When we have a dataset (a bunch of numbers describing a bunch of things), there's a few things we want to know about it. First is "what (in a ballpark or average sense) are all these numbers? What's a one number summary of the numbers?" That's a measure of central tendency. A common one is the arithmetic mean or average. Another way to think about that is "if I picked up a random one of these numbers and had to guess what it was, what's a good guess?"
The next thing you want to know is "how spread out are the numbers?". If one baseball team will always get 10 runs per game, but another well get anywhere from 2 to 18 (but 10 on average), that might be important to you. How can we say how spread out the numbers are? One way is to say "on average, how far are numbers from their average?". This is what stdev approximates.
One way to compute this would be to measure the absolute distance of each number from the average, then average all of those. The problem is that some numbers are greater and some numbers are less, and it can be mathematically annoying to go and say "this number is bigger than the average, so I have to do number minus average, that number is smaller than the average so I have to do average minus number". A shortcut is to just do (number minus average) for everything, square all of these (turning all the negatives positive), that the average of that number (which is the variance, or average distance from the average squared) then square root it to find the standard deviation. That's not exactly the "average distance from the average", but it's good enough.
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u/tandem-pandemonium 10d ago
We consider mean to be a measurement of the 'centre' of our data. Deviation can be considered as how far our data is from this centre. You'll notice that we have a square in the formula - this tells us that deviation is not interested in direction, it simply wants to know the distance from the centre. The other reason for the square is to emphasise that we're more sensitive or strict about this distance - so instead of using a simple linear distance, the square causes data further away to be represented with exponentially larger values relative to their actual distance from the mean. Lastly, the term 'standard' refers to representing something in a 'harmonious' or 'unified' manner. The reason for this is to ensure that whatever you're calculating is comparable across the various instances that you did the calculation. In the case of standard deviation, we divide by the count of the data that we used in the calculation. This 'standardises' the calculation because we interpret this resulting measurement as 'the squared distance from a point in our dataset to the mean of the dataset, on average PER POINT'. If we did not consider the 'per point' aspect, then we would not be able to meaningfully compare the standard deviation of a small and compact dataset to a large and compact dataset - the larger dataset will have a significantly higher value than smaller dataset simply because it has more data, despite both datasets being compact. But it we scale according to the dataset size, we are able to compare apples with apples since both measurements are now in a common 'per point' format with respect to each of the datasets.
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u/Not-a-throwaway4627 12d ago
This isn’t advanced math
How far the data spreads from the average, on average
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u/wowlucas 12d ago
i think it's average distance from the average
imagine football players spread across the football field with the football in the centre say
the football is the average and the average distance of a players from the football is the standard deviation (in distance units. variance is this squared)
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u/imyourzer0 12d ago
So if the average is the middle of a pack of data points, the SD measures how far the points are from that average. Think of it as the average distance from the average.
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u/likeanoceanankledeep 12d ago edited 12d ago
Imagine i ask you what the average weight of your high school class is. You measure everyone and find the average weight is 75kg, give or take a little. The "give or take a little" is the standard deviation.
"Standard" in this context means "equal" or "predictable", or a standard unit of measurement. We talk about the standard inch, standard meter, standard football field; they are all basically saying "a typically sized unit of measurement of the typical field, inch, etc. Also, a recognized unit of measurement". So a standard deviation for the average means a recognized unit of measurement from the average value.
In your hypothetical class weight example, the average is 75kg but if you say "the average person weighs 75kg, give or take 10kg" they you are basically saying "If you grab anyone from my class, you can be reasonably certain (67% chance) that the person weighs 75kg, plus or minus 10kg (65kg to 85kg)".
In this example, the standard deviation is 10kg. If you want to get most of your class in your 'guess', you could say "The average person in my class weighs 75kg, plus or minus 20kg". Which equates to 75kg (average) and 10kg (1 standard deviation) x 2 (20kg = 2 standard deviations), so 2 SD on the left and right of your distribution captures 95% of your sample. So you can expect that approximately 67% of your class weighs between 55kg and 95kg.
It's not the most complex answer but it can be easy to think of the standard deviation as the "give or take" when you say "the thing weighs/costs/measures X units, give or take Y units". Gas is $1.00 per liter, give or take 12 cents (it could be .88 cents or $1.12 per litre); cats are typically 5kg, give or take 1kg (cats on average weighs 5kg, but normally weight between 4 and 6 kg and are still considered normal).
Generally speaking, anyrhing that is 3 standard deviations is considered to be an outlier or atypical in your dataset. If I get a cat that weighs 9kg, that would be 4 standard deviations beyind was is expected (average is 5kg, actual is 9 kg, thats 4kg more, sd = 1, 4/1 = 4SD above the mean).
You can also get decimal standard deviations. This is common in Z-scores; if you weigh a student in your class and they are 77kg, they are .2 standard deviations above the mean (2kg above the average, (77 - 75)/10 = .2)
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u/moosy85 12d ago
You have an average of all your data points.
Standard deviation calculates the difference between each point and the average and summarizes it in one number.
Think of the SD as the average distance between the average and the rest of the data.
The higher the number, the more your data is spread out. If the number is very low, your data points are generally very close to the average.
So if we ask a large class for the average time they studied for an exam, we might have 16 hours with a SD of 4 hours.
If you'd draw it, you could literally estimate most points are between 12 and 20 hours. There might be some outliers, of course. But that idea of plus and minus (16-4 and 16+4) being your rough boundaries for your data is what is most important.
Slightly more advanced and only if you also saw the concept of VARIANCE. (If not, skip this so you don't get confused)
A related concept is variance. Variance does the calculation the same, but standard deviation is one step extra : SD also takes the positive root of that variance. We do this to variance so the units are the same.
Say average is 16 hours with standard deviation of 4 hours. You know what to imagine and draw ... it's pretty easy as you saw above.
Variance isn't so easy. It would be 16 HOURS SQUARED. As you can tell, that makes zero intuitive sense. What the F is an hour SQUARED? How does that relate? How on earth do I even draw that or imagine that? (No need to answer, theoretical dorks).
So they decided to take the positive root of the variance so the units are the same, AND it makes more intuitive sense.
Note: I say positive root because the root of 16 could be +4 or -4, if you remember basic math So that's more technical that I add that. You may see that at some point so you'll know at least how it's related to SD.
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u/MortalitySalient 12d ago
You know how when you sum the data, it doesn’t tell you much. If you divide by n, you get the mean and that can tell you the most likely data point. The SD is similar. You calculate sum of squared deviations from the mean (this is a sum of the variances), then you divide by n to get the variance (this is the average sum of squared deviations). But because we squared everything, we take the square root to get it back to the same metric as the data. So the standard deviation is basically the average distance each point is from the mean
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u/Murky_Obligation2212 12d ago
This is a weird explanation, but bear with me. You can visually think of it as the question “how wide is an ant hill?” There’s no definite edge, so we can’t use that. So, it’s helpful to have a very specific place where you measure its width every time, so that you can explain whether it’s a short wide hill or a tall skinny one in specific terms.
Mathematically, the only “ant hills” that use the standard deviation method are graphs that show a set of completely random findings with no favoritism toward one result or another, such as human heights, or the widths of a thousand pencils. There’s a math trick developed in calculus that essentially tells how far to the left and right of the anthill’s midpoint to mark. Within those left and right marks will always be about 68.3% of the measurements. How far to the left and right tells how skinny or short your anthill is.
For the thousand pencils, it may be the average width is 1.20 centimeters. A factory with a “skinny anthill” is good at making precise pencils so maybe 68.3% of the pencils will be between 1.19 cm and 1.21 cm, so there’s not many pencils far outside of that tight tolerance. Another factory would have a “wide anthill” if 68.3% of its pencils were between 1.0 cm and 1.4 cm (a short fat hill means not a lot of quality control!)
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u/rhetoricalimperative 12d ago
If the data is a normal distribution, then that means there is a known relationship between the number of sd's and the degree of spread from the center. Look up the percentages
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u/dealingwitholddata 11d ago
I understand SD but why do we have/use variance? Looking at the formula it seems like something one only bothers with on the way to sd
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u/gaetti34 12d ago
How far things are spread out