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# Questions tagged [standard-deviation]

Standard deviation is the square root of the variance of a random variable, an estimator thereof, or a similar measure of the spread of a batch of data.

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### Why square the difference instead of taking the absolute value in standard deviation?

In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can't we just simply take the absolute ...
50k views

### Why is sample standard deviation a biased estimator of $\sigma$?

According to the Wikipedia article on unbiased estimation of standard deviation the sample SD $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \overline{x})^2}$$ is a biased estimator of the SD of the ...
99k views

### Difference between standard error and standard deviation

I'm struggling to understand the difference between the standard error and the standard deviation. How are they different and why do you need to measure the standard error?
371k views

### What is the difference between a population and a sample?

What is the difference between a population and a sample? What common variables and statistics are used for each one, and how do those relate to each other?
14k views

### How to perform Student's t-test having only sample size, sample average and population average are known?

Student's $t$-test requires the sample standard deviation $s$. However, how do I compute for $s$ when only the sample size and sample average are known? For example, if sample size is $49$ and sample ...
10k views

### Standard deviation of binned observations

I have a dataset of sample observations, stored as counts within range bins. e.g.: min/max count 40/44 1 45/49 2 50/54 3 55/59 4 70/74 1 Now, ...
19k views

### Variance of a bounded random variable

Suppose that a random variable has a lower and an upper bound [0,1]. How to compute the variance of such a variable?
6k views

### Can we use leave one out mean and standard deviation to reveal the outliers?

Suppose I have normally distributed data. For each element of the data I want to check how many SDs it is away from the mean. There might be an outlier in the data (likely only one, but might be also ...
231k views

### How to 'sum' a standard deviation?

I have a monthly average for a value and a standard deviation corresponding to that average. I am now computing the annual average as the sum of monthly averages, how can I represent the standard ...
28k views

### Standard deviation of standard deviation

What is an estimator of standard deviation of standard deviation if normality of data can be assumed?
4k views

### Why are we using a biased and misleading standard deviation formula for $\sigma$ of a normal distribution?

It came as a bit of a shock to me the first time I did a normal distribution Monte Carlo simulation and discovered that the mean of $100$ standard deviations from $100$ samples, all having a sample ...
11k views

### What is the standard error of the sample standard deviation?

I read from there that the standard error of the sample variance is $$SE_{s^2} = \sqrt{\frac{2 \sigma^4}{N-1}}$$ What is the standard error of the sample standard deviation? I'd be tempted to guess ...
11k views

### Maximum value of coefficient of variation for bounded data set

In the discussion following a recent question about whether the standard deviation can exceed the mean, one question was raised briefly but never fully answered. So I am asking it here. Consider a ...
8k views

### Adding coefficients to obtain interaction effects - what to do with SEs?

I have a multivariate regression, which includes interactions. For example, to get the estimate of the treatment effect for the poorest quintile I need to add the coefficients from the treatment ...
100k views

### Is it possible to find the combined standard deviation?

Suppose I have 2 sets: Set A: number of items $n= 10$, $\mu = 2.4$ , $\sigma = 0.8$ Set B: number of items $n= 5$, $\mu = 2$, $\sigma = 1.2$ I can find the combined mean ($\mu$) easily, but how am ...
152k views

### How do I calculate a weighted standard deviation? In Excel?

So, I have a data set of percentages like so: ...
7k views

### Normality of residuals vs sample data; what about t-tests?

An addition to the common confusion about normality testing in inferential statistics for general linear models: I understand the assumption of normality refers to the residuals in ANOVA and ...
128k views

### What does the size of the standard deviation mean? [duplicate]

According to Wikipedia (my emphasis), In statistics, the standard deviation ... is a measure that is used to quantify the amount of variation or dispersion of a set of data values. A standard ...
718k views

### What's the difference between variance and standard deviation?

I was wondering what the difference between the variance and the standard deviation is. If you calculate the two values, it is clear that you get the standard deviation out of the variance, but what ...
4k views

### How can I find the standard deviation of the sample standard deviation from a normal distribution?

Forgive me if I've missed something rather obvious. I'm a physicist with what is essentially a (histogram) distribution centered about a mean value that approximates to a Normal distribution. The ...
1k views

### Why does this excerpt say that unbiased estimation of standard deviation usually isn't relevant?

I was reading on the computation of the unbiased estimation of standard deviation and the source I read stated (...) except in some important situations, the task has little relevance to ...
59k views

### Understanding “variance” intuitively

What is the cleanest, easiest way to explain someone the concept of variance? What does it intuitively mean? If one is to explain this to their child how would one go about it? It's a concept that I ...
31k views

### Transform Data to Desired Mean and Standard Deviation

I am looking for a method to transform my dataset from its current mean and standard deviation to a target mean and a target standard deviation. Basically, I want to shrink/expand the dispersion and ...