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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6 views

What quantifies a stable parameter?

I'm optimizing 5 parameters for an option pricing model. Now I want to asses whether these parameters are stable over time (i.e., a year). For this I create about 12 subsamples and estimate the ...
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16 views

Creating a weighted average from different summary statistics and measures of dispersion

Four published clinical trials reported the average age in years of the patients enrolled in the study. Three trials reported a mean and one reported a median. They also reported some measure of ...
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26 views

Standard deviation of a sample when you know the average

I'm coding an app, a part of which is graphing values from a database. The graph plots the average value of every 10% of the values up to 100% so there are ten points along the x-axis. The graph ...
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1answer
11 views

Measure of intermittency/continuousness of a signal

I have three signals (below) each having the same standard deviation, however, are clearly very different temporally. Is there some such metric that could be calculated for each of these signals to ...
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1answer
25 views

Combining results of two samples to find combined standard deviation

I was making an attempt to solve the following problem sets, however, my answer 15.913 seemed quite different from that in the answer key 16.84. I have checked my answer a few times and re-doing the ...
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31 views

Calculation of standard variance $s^2$

First picture is the question and its answer key: The second picture is my solution: I know that $S^2=\frac{\sum(x_i-\bar x)^2}{n-1}$ But in the answer key, $s^2$ cannot be found in that way. ...
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1answer
21 views

Calculating scale mean from item means

I'm working on a review paper and need to collect the means and standard deviations of a given measure (such as a measure of depression) from papers of interest. However, some authors report means and ...
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0answers
43 views

Standard deviation of normalized data

I have a data set $y_i$ (where the $y_i$ are photon counts in time period $i$, $i=1,2,...,n$, assumed Poisson), with an estimated standard error $s_i$ (= $\sqrt{y_i}$) for each count. For some ...
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1answer
40 views

Which error is displayed in an error ellipse?

I have some bivariate data and I have calculated the error ellipse in the following way: I have first calculated the covariance matrix and then to obtain the radii of the ellipse I have taken the ...
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159 views
+50

Standard deviation of several measurements with uncertainties

I have two 2 hours of GPS data with a sampling rate of 1 Hz (7200 measurements). The data are given in the form $(X, X_\sigma, Y, Y_\sigma, Z, Z_\sigma)$, where $N_\sigma$ is the measurement ...
2
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1answer
35 views

How to convert mean and standard deviation to a single meaningful and quantifiable value?

I look at mean and standard deviation of various map like data and each give meaningful information but sometimes they provide different information. For example, let's take states in a country. One ...
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3answers
86 views

Unbiased estimate of population standard deviation: is sqrt(2) a superior correction?

Background on bias correction constants The standard deviation is calculated like this: $$ SD = \left(\frac{1}{N-constant} \sum_{i=1}^N (x_i - \overline{x})^2\right)^{1/2} $$ Following Wikipedia's ...
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27 views

$\sigma^2 \le (\mu-a)(b-\mu)$ for all probability distributions bounded on $[a,b]$? [duplicate]

Let $\mu$ be the mean and $\sigma$ the standard deviation of a probability distribution defined on the bounded interval $[a,b]$ (that is, the probability that the random variable lies outside $[a,b]$ ...
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0answers
23 views

Standard mean and deviation

A company supplies specialized high-tensile pins to a customer.It uses an automatic lathe to produce the pins.Due to factors such as vibration, temperature and wear and tear, the lengths of pins are ...
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0answers
21 views

Validity of standard deviation

I have a total of 7 data sets that i want to compare. Each set has 2 samples only, for which i want to calculate standard deviation. Will my value of standard deviation be reliable? Or is it a a ...
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15 views

Standard Deviation Grows Quadratically with Input Variable

I take an input x, based on which I do an experiment that gives me several data points. I compute the standard deviation of these data points. Then, I change ...
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1answer
33 views

Standard deviations and significance values

I was wondering if data 2 SD from the mean is deleted as outliers, is it possible there after to report 0.01 significance values? Thanks!
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1answer
44 views

Find minimum number of batteries to last a week with 95% probability given mean and sd of lifetime

A TA needs a very important program on his computer but his power cable is missing. Luckily, he happens to have 100 batteries lying around and a contraption that can store batteries to use one at a ...
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2answers
55 views

SD larger than mean, non-negative scale

I was given an article reporting a study very similar to one my lab wishes to run. But, I noticed that for the variable of interest, Duration, the SDs are larger than the mean...since this is ...
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35 views

Confidence interval when data is in range

I am trying to calculate the confidence interval when data is given in range. Example: Rather than telling their exact age in years, 9 sample students from a class tell their age as: (23 ...
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1answer
111 views

What are the relative merits of Winsorizing vs. Trimming data?

Winsorizing data means to replace the extreme values of a data set with a certain percentile value from each end, while Trimming or Truncating involves removing those extreme values. I always see ...
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36 views

Standard deviation of a dataset comprised of triplicates (industrial stack sampling data)

I have 4 triplicate data values. each consist of 3 values, for example, this could be 1: Concentration: 45 78 66 These data have a mean of ...
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0answers
9 views

comparing variation of a blended product from populations of different sizes (dilutions)

Original question: If population 1 consists of blended piles of size X_1 and population 2 consists of blended piles of size 4*X_1. Should I expect the standard deviation of X_1 to be equal to 4*the ...
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1answer
44 views

Is it ok to compute statistics on t-values?

Background I have a population in which my dependent variable is binary with a highly-skewed distribution: Very few records are 1 (doers), most records are 0 (non-doers). I'm using logistic ...
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1answer
14 views

Standard deviation for values below 1

When analyzing a dataset based on percentages, I have on occasions worked with data as "full" value (i.e. "50") or "reduced" value (i.e. ".50"). However, it just occurred to me that this could have a ...
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15 views

Calculate Standard deviation from mean and confidence interval (95%) in R [duplicate]

I have some data with mean and confidence interval at 95% exclusively (I do not have the rough values), and I would like to calculate the Standard deviation of these population. For example: ...
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3answers
882 views

Why does the standard deviation not decrease when I do more measurements? [duplicate]

I made 100 measurements of a certain quantity, calculated mean and standard deviation (with MySQL), and got mean=0.58, SD=0.34. The std seemed too high relative to the mean, so I made 1000 ...
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1answer
37 views

lognormal distribution, standard-deviation and (physical) units

I have a distribution of microparticles that follows a lognormal distribution. The cumulative distribution function thus is given by: $$ F_X(x;\mu,\sigma) = \frac12 ...
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48 views

ldentifying observations on the edges in heteroscedastic data

Consider bivariate data consisting of correlated variables (r ~ 0.9). It is known how both the variables are calculated. Each observation is identically distributed but non independent. Also, the ...
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1answer
26 views

What are RMSE SD and Rsquared SD metrics in resampling results using R package:caret?

I've been doing predictive modelling with R package caret. When resampling regression models, I get the traditional RMSE and Rsquared metrics, but also RMSE SD and ...
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1answer
33 views

Is variance replacing square of standard deviation in a t test?

I am writing a t test using the code here : How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data? But I would like to use the root of the variance as an ...
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17 views

Linear Mixed Model Construction Suggestion

I'm currently working on some data that requires me to use linear mixed model. Explanation of Data Experiment of Drugs on Mouse I have 3 drugs and 1 control Unbalanced number of mouse for each ...
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15 views

Calculating variation of one variable within one experiment

I am conducting a preliminary study, where people assess (7-point likert scala) different pictures. Besides asking for my 2 Independent variables (which are the manipulations for my main study, an ...
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22 views

Standard error of the mean in a repeated measures study

I am having difficulty figuring out how to calculate the SEM and report it in a table. I have 5 different time periods, and for those time periods 6 different measures of digestibility for each ...
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1answer
62 views

When is the standard error of the mean impossibly large for a given data range, when we know the sample size?

While reading an article (published and peer-reviewed, referenced below) investigating proportions of different tissue types in the human brain I came upon a table presenting data on the different ...
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1answer
69 views

Given a mean and 95% confidence interval, do I need to know the sample size to calculate the standard deviation?

This question regards the basic statistics of a normal distribution, but I can't figure it out. I have been given the mean and 95% confidence intervals for a distribution, but would like to know the ...
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267 views

When is a sample proportion p hat instead of x bar

I just started my first statistics class and am not majoring in statistics so sorry if this sounds like a beginner question and also sorry if my language is incorrect. (feel free to correct me.) I ...
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22 views

Error propagation calculation yielding negative variance

I am trying to calculate the standard deviation of the sum X = A + B. A and B are mean values, and I do not have access to the source data. A is 0.46 with an SD of 0.014 (SDa) and B is 0.375 with an ...
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13 views

How to measure the variance from reading to reading

I have some values being read by physical sensors. Two of the values from nice lines which are very clear, but the third is all over the place. The problem is calculating a metric to show that the ...
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31 views

Combining forecast from ARMA models

I have three ARMA(p,q) models for the variable X and using each model I produce forecasts for 12 months ahead. Note that in all three models the residual is normally distributed. Now if I want to ...
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17 views

Statistical test for zero valued variable

I am testing a product (liquid bag) for leakage and my primary variable is the amount of leakage in ml. I have a specification that states, on average, leakage must be below XXml. In total I tested 20 ...
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85 views

Variance of sample proportion decreases with n but of a count increases with n - why?

I've got an intuitive block with this. For a binomial problem, the standard deviation of a count is $\sqrt{np(1-p)}$. Conversely, the standard deviation of the sample proportion decreases with ...
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2answers
60 views

Which measures of statistical dispersion should be used to estimate dispersion of slope of a trendline

Although I know how to calculate many of the statistical values, I have some difficulties understanding which one should I use in a specific situation. Here is my example: In my experiment I tried to ...
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1answer
56 views

Business Statistics [closed]

a teacher gives a 15 item science test. for each item, a student receives one point for a correct answer; 0 points for no answer; and loses one point for an incorrect answer. total test scores could ...
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1answer
50 views

Standard deviation of recall, precision, accuracy and F-score?

I'm not sure how to correctly calculate the standard deviation of recall, precision, accuracy and F-score. For example: ...
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4answers
309 views

Intuition behind standard deviation

I'm trying to gain a better intuitive understanding of standard deviation. From what I understand it is representative of the average of the differences of a set of observations in a data set from ...
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30 views

Error Propagation vs Standard Deviation

Say you have a set of data of lengths, widths, and heights of a rectangular box. Why do we have to use error propagation to calculate the std. dev. of the box's volume? Why couldn't we calculate the ...
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19 views

Standard deviation of lift

I am trying to calculate the standard deviation of lift given treatment and control groups, and the respective response values, which are binary, for each entity in the groups. Here is the problem in ...
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1answer
57 views

standard deviation help please!!! [duplicate]

a tire manufacturer believes that the treadlife of its snow tires can be described by a NOrmal model with a mean of 32 thousand miles and standard deviation of 2.5 thousand miles. Based on this ...
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1answer
95 views

What am I really calculating here?

This is partly related to the question at Visualising the variance which I haven't accepted an answer yet, partly because I have become unsure if I'm asking the correct question. The case is this, we ...