In Probability and Statistics, the standard deviation of a statistical population or data set is a measure of how much variation or dispersion exists from its average value. It is defined as the square root of the variance.

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hypothesis testing two sample problem and standard error of mean

In my homework, I was asked to find the standard error of mean for 2 cases and then do the 5% and 1% test for both of them. I know how to work out stand error of mean, but I don't know how to use it ...
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X and Y are two random variables, what is the standard deviation of X - 2Y

I have: E(X) = 10 E(Y) = 12 Var(X) = 4 Var(Y) = 9 covariance = 2 I know that for: ...
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Population deviation\Sample deviation

I am really stuck in checking weather something is a sample of the entire population or it is infact the polution. Suppose I make a bucket to hold a litre of water and I obtain 8 measurements to ...
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Difficulty to find the Standard Error in a simple hypothesis testing

I'm having some difficulty to solve a very simple hypothesis testing problem. $$\begin{array}{c|c|c|} & \text{X} & \text{Y} \\ \hline \text{1} & 1 & 1 \\ \hline \text{2} & 3 ...
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Relationship between median and standard deviation

I have some data and I added Gaussian noise with zero mean ($\mu=0$) and standard deviation ($SD=SD$). I was interested to see the behaviour of the noise to the data after integrations. I integrated ...
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Why does variance divide by $n-1$? [duplicate]

The variance is: $$\dfrac{\sum_{i=1}^{n}(x_i-\bar x)^2}{n-1}$$ I read that $n-1$ is used instead of just $n$ when we are measuring the variance of a sample taken from a bigger population. I don't ...
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Why is variance squared?

The mean absolute deviation is: $$\dfrac{\sum_{i=1}^{n}|x_i-\bar x|}{n}$$ The variance is: $$\dfrac{\sum_{i=1}^{n}(x_i-\bar x)^2}{n-1}$$ So the mean deviation and the variance are ...
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question about Mean absolute deviation formula

$$\frac{\sum_{i=1}^{n}(x_i-\bar x)}{n}$$ This method will not work for calculating the mean deviation. Instead we have: $$\frac{\sum_{i=1}^{n}|x_i-\bar x|}{n}.$$ I'm not quite understanding why ...
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Standard Deviation ( Sort of ) Problem

I have a bunch of particles spread over a 2D area. I plan to fit a a distribution to describe the spread. To start off : I have about 100 particles arranged in a circular pattern in a "unit" ...
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Model selection: geometric mean of the standard deviation.

I have two models that represent a physical process. To determine which model is the best, I make some experiments and compare measured data with data predicted by each of the models. The model with ...
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Where are they getting this number from?

Here's the question that I'm having a problem with: ...
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Constructing confidence variances for std and variance samples.

A) Construct the 90% confidence interval for the standard deviation for the dark treatment. B) Construct the 95% confidence interval for the variance for the sunlight treatment. And that what I ...
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579 views

Probability and proportion from standard deviation and mean [duplicate]

I do not know how to start this problem-help needed-kindly help me The lifetimes of a colour TV picture tube is normally distributed, with a mean of 8 yrs and a standard deviation of 2 years. ...
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Why square the result of $x_1 - \bar{x}$ in the standard deviation? [duplicate]

I don't understand the necessity of square the result of $x_1 - \bar{x}$ in $$\sqrt{\frac{\sum_{i=1}^{N} (x_i - \bar{x})^2}{N-1}}$$. In fact I don't understand even why is $N - 1$ on the denominator ...
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25 views

Evaluating Data

I have a set of data that I need to evaluate. The data came from 15 people we asked to evaluate several project proposals using 6 different criteria. For each weighted criteria, they selected 1 of 4 ...
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Any way to simplify this expression?

So I have a vector of asset allocation weights given by $x \in R^4$ and a covariance matrix of the asset returns $\Sigma \in R^{4,4}$. I know by the spectral theorem, $\Sigma = V DV^{-1}$ and the ...
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Does it make sense to use zscore values with multiple confidence intervals?

I have a program that takes a historical dataset (e.g. muffins sold in the last week), calculates the zscore of the current value, and determines whether or not the current value is abnormal based on ...
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108 views

Using Least Squares method to determine unknown variables

Hey guys my next test is coming up and my professor gave us a study guide that we "should" be able to compete. Here is one of the questions I don't know how to attack: I dont just want an answer. I ...
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122 views

Determine the distribution underlying several given scores and their percentiles

I am trying to build a FICO score calculator that estimates one's FICO score given one's percentile from another credit report. FICO score data is kept fairly secret, but the following information is ...
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investigating a relationship at $5 \% $ level significance

$n=12$ $\bar{x}=? $ sample average = $\sigma $ standard deviation = $\alpha =$ $H_a :$ Degrees of freedom if applicable Critical value(s) = Sample mean Standard error of mean = $\frac{\sigma } ...
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36 views

Std Dev of large set

Lets assume we have a router that transmits packets at 24,000 bytes/msec and that packet lengths are uniformly distributed between 100 and 1,500 bytes. Packets are incoming to the router at a rate of ...
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291 views

Statistics: how does standard deviation measure quality - please answer everyone?

There are many types of measures of variation/dispersion from the mean, but standard deviation can be confusing. If we are measuring error/variability, then 1σ is better than 2σ. That is to say that ...
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Why the natural log is there in MLE?

Why do we use natural log for MLE?
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In calculating the standard deviation, why do we square the difference from the mean, as opposed to cubing? [duplicate]

This question has been bothering me for a while: In calculating the standard deviation, why do we square the difference from the mean, as opposed to cubing the differences (and then taking the cube ...
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319 views

How to calculate Standard Deviation without detailed historical data?

i'm taking some measurements... Let's say i don't have the luxury to store each individual value but i can only store the sum of all measures and their number (and any other such aggregate data). For ...
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Standard Deviation result wrong or right

I made two scripts in PHP to calculate the standard deviation. But I am not sure if it works correctly both of my scripts have different results. first script 1,2,3,4,5,1 = 1.5 second script ...
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Have averages, need variance

I have a large spreadsheet, generated by a colleague, that contains the results of $E$ experiments. For each experiment, he calculated the average of $M$ measurements. I need the calculate the ...
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Standard deviation / Bell Shaped Distribution

In a forest, it is known that the circumference of 10 year old oak trees when measured three feet above the ground is 20 inches with a standard deviation of 4.5 inches. It is also known that these ...
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106 views

Why is the expected value of the squared value equal to the sum of the standard deviation and the mean?

I am currently reading the proof here that one has to divide by $n-1$ in order to get an unbiased estimator of the population variance. What I do not get is this: \begin{equation}E[y_i^2] = \sigma^2 ...
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standard deviation of a rate of phone calls

I am trying to implement some real time monitoring. I have a real time data feed from which I can calculate the number of phone calls received in the last hour (now-60 minutes). I want to alert when ...
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90 views

Why is my sample standard deviation not an unbiased estimator?

I was goofing around with a spreadsheet and decided to show empirically that the sample standard deviation is an unbiased estimator of the true population standard deviation. Link to Excel File I ...
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57 views

Standard deviation and intervals

I'm working on some homework and I'm stuck on a question that is not making sense to me in terms of my answer. The question states: ...
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62 views

Chebychev to get at least 90 %

Im am given a list of integers and asked to give the interval that contains at least 90 % of my values. Values : $62,56,72,83,66,77,62,71,50,58, 74,81,76,67,70,70,69,67,80,81, ...
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Writing a deviation from optimal formula

I really dont know how to write it as a proper mathematical formula instead of text, could you please help? Basically I have two formulas and apparently I they are not Mathematical.. Formula ...
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Standard Deviation Question

My working out: Median = mean = 60 Q3 = 25% of values at 75 25% = 0.25 = z-score of 0.68 Sx = (75-60)/0.68 = 22.3881 approx = 20... I said D The correct answer is B. 10
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Weighted mean from a set of average and standard deviation pairs

I'm trying to replicate some math a professor did related to Twitter sentiment analysis. Basically, there is a sentiment dictionary, called ANEW, that contains a mean and standard deviation for 3 ...
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155 views

Standard Deviation for Normally Distributed Bell Curve - Worded Problem

My working out: Z = (14-9.5)/2.25 = 2 % less than 2 = 95% Answer is 97.5 % .... no idea...
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Is Standard Deviation the same as Entropy?

We know that standard deviation (SD) represents the level of dispersion of a distribution. Thus a distribution with only one value (e.g., 1,1,1,1) has SD equals to zero. Similarly, such a distribution ...
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Summing up Standard Deviations - best approximation

For a long data series the overall Standard Deviation shall be collected. However, due to memory constraints the data has to be aggregated per day - in a way that only one number is stored per day ...
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105 views

Given Standard Deviation and Population size, how can I calculate the number of population at mean

As per the title, I'd like to calculate the number of the population at mean, given a std.dev and population size. The use case for this, is Mobile Phone push notifications. I send the notification ...
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34 views

How to answer probability question with basic std dev statistics

I have a data sample, say: $69$, $72$, $100$, $87$, $57$, $123$, $110$. Knowing the standard deviation and the mean what is the answer to the question: What is the number ($x$) for which $n\%$ out ...
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Question about an article by Nassim Nicholas Taleb about the problems with standard deviation.

The article by Nassim Nicholas Taleb says that using standard deviation is flawed and is poorly understood and mean absolute deviation should be used. Because this article is short, and I don't ...
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Standard deviation: When to use which sum-coefficient?

I'm wondering when to use $\sigma = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n}(X_{i}-X_{mean})^2}$ and when to use $\sigma = \sqrt{\frac{1}{n} \sum_{i=1}^{n}(X_{i}-X_{mean})^2}$ which I have both seen in ...
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How is the Standard Error and the Unbiased Estimate of the Variance Related?

I am going through a statistics textbook and there are two similar formula's that I cannot seem to grasp, one under the "Sampling Error" section and the other under the "Unbiased Estimator" section. ...
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Find the variance of $x$ when the standard deviation is given in the form of $ax+b$.

The standard deviation of $3x+7$ is $4$; then what is the variance of $x$? I know that variance is the square of the standard deviation but how does $3x+7$ and $x$ relate?
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Rolling standard deviations

I am trying to calculate standard deviations on an array of numbers. My psuedo code looks like this: ...
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can STD of subsets be used to arrive at the STD of the whole set

Assuming I have a set of values called S and the STD of S is Xs. Let's say I split S into two subsets S1 and S2 with standard deviations X1 and X2. The number of elements in S1 and S2 are called W1 ...
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The rule of the 3 sigmas -— how many times multiply the sigma to get 85%?

$\sigma c=\sqrt{\overline{R}(\sigma S)^{2}+\overline{S^{2}}(\sigma R^{2})}$ where, $\sigma c$ --- the buffer stock --- needed for maintaining the risk of stockouts, is used by logistitians ...
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Confidence interval and normal distribution

For question (a), is the answer 0.7143? For question (b), is the answer 10.85 and 11.95 ?