Questions tagged [standard-deviation]

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. Use this tag alongside (statistics).

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Calculating a sample size

I can't figure out how to crack this problem. It's as if I don't have enough information. Walk me through please Jogging is a popular sport in Brilliantia. According to a recent survey, between 80% ...
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Infinite Standard Deviation with Kalman Filter

I'm using a Kalman Filter code on Matlab that produces the results of Stock and Watson 1991 with some macroeconomic variables, GDP and a soft indicator to forecast the economy of a country (everything ...
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Can you calculate (or estimate) standard deviation using mean, median, and sample size? [closed]

If you know the mean, median and sample size (with no other information), can you estimate standard deviation? Or, let's say you know one value from the sample (only 1), can you tell which percentile ...
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Finding the underlying distribution and standard deviation given percentile values

Is there a way to find the underlying distribution and the standard deviation given the data below? Obviously it is not normal as it is not symmetrical. It is also truncated at 0 as there is no ...
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the mean and standard deviation aren't the same as those of the input data i provided after sampling

have a log-normal mean and a standard deviation. after i converted them to the underlying normal distribution's parameters mu and sigma, I sampled from the log-normal distribution however when i take ...
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probablity man is taller than woman in random pair (or comparing random values from distinct normal distributions) [duplicate]

General Question Suppose two populations follow normal distributions for some variable, with population $A$ given by mean and standard deviation $\mu_A$ and $\sigma_A$, and population $B$ given by ...
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How to measure the ranking deviation of a matrix of elements

I have elements in a table as seen here: Experiments 1st place 2nd place 3rd place 4th place 5th place 1st run Element20 Element23 Element10 Element13 Element0 2nd run Element23 Element27 Element10 ...
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I thought var(a) * var(b) = var(ab) but, it is not? (independent each other) [duplicate]

Let's say that we have two independent variables, r, and g. If two variable is independent, Var(r) * Var (g) should be Var(r*g). However, as shown below, It is not. I do not understand why Var(r*g) is ...
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Standard Deviation and data set increasing by multiplication.

Hi guys I recently started learning statistics and I'm a bit confused. I know when a data set is multiplied by a constant, its standard deviation and mean is multiplied by the same number. However ...
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How can I derive the general formula for the standard deviation of an arithmetic series?

According to this wikipedia article, the standard deviation of an arithmetic series has the following formula, in terms of the common difference $d$ and number of terms $n$. The article does not cite ...
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Sample Mean vs. Population Mean

I'm having trouble understanding what exactly is meant to be found given the information presented. Obviously, the answer will be a value found on the z-table and the probability of this event ...
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Standard error of the mean for different experiments

I am confused about the calculation of the SEM when one performs multiple independent experiments. Suppose we perform $k$ different experiments obtaining means $\mu_k$, standard deviations' $\sigma_k$ ...
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Obtain standard deviation from sum of values

I'm looking for a way to obtain the "composed" mean and standard deviation of two (related) datasets. So let's assume I have n = 25 recordings of one characteristic (x) and the same number ...
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Regression, can someone help me understand this equation?

The criterion for mapping the individual test case to the four ideal functions is that the existing maximum deviation of the calculated regression does not exceed the largest deviation between ...
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standard deviations for mean vs for predictions

I work in finance and wanted to ask a quick question regarding standard deviation of data sets. I have collected data sets over the last 10 years and would like to use them to make a prediction for ...
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Using s to estimate $\sigma$ when finding the sample size in confidence interval questions

I am trying to learn sample confidence interval for $\mu$ , in this topic , there is a subtopic which is finding the sample size. I know that if $\sigma$ is given (standard deviation of population) , ...
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Standard deviation of a joint probability distribution.

I have the joint distribution. This is how many packages of toilet paper, $\mathbf{T}$, and packages of wipes, $\mathbf{W}$, a shopper can obtain per visit. I'm being tasked to find the standard ...
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How precise when reporting mean and standard deviation?

Can anybody confirm that my reasoning for the incorporation of the number of decimals is correct here? I want to calculate the area A of a rectangle with length = 13.727 m and width = 43.313 m. ...
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Precision and significant digits in reporting standard deviation

I have 4 measurements: 40.1714, 40.1718, 40.1721 and 40.1725. The calculated standard deviation is 0.00046547466812633. With which precision (number of decimals) do I report this number as "mean +...
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How to calculate the standard deviation of a variable

I have determined the slope of a linear fit and its standard deviation. Now I need to calculate k, which is 1/slope, but I don’t know to calculate the standard deviation of k. Is it 1/standard ...
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standard deviation of piecewise function

Let $X$ be a random variable, with probability density function $f(x)= \begin{array}{cc} \{ & \begin{array}{cc} \frac{3}{4}(1-x^2) & -1\leq x\leq 1 \\ 0 & \text{...
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Standard normal distrubtion, standard error

According to data obtained by a management consulting firm, the mean working hours per week for accountants in a country is 48 hours, with a standard deviation of 7 hours. Let X be the number of the ...
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Given the stdev of a dataset and the stdev of a subset, compute the stdev after the subset is removed

I am given a set of basic metrics for a dataset, such as: mean standard deviation length I am then given the same set of metrics for a subset of the dataset, for example, a set of outliers. However, ...
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Why is Standard Deviation Calculated With the Square Root of the Sum of Squares Instead of Sum of Square Roots of Squares

The standard deviation definition I saw in my textbook and heard in the lessons is that it is a measure of how spread-out a data set is and as such it calculated as the mean of the distances between a ...
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How to evaluate the difference/distance between 2 values positive and negative on a scale

Problem 1 : The input is 2 values, that can be in a scale between [-3.89, 10.66] And i need to compare the difference between an oldValue (A) and a newValue (B). So i want to create a variable that ...
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Standardising third moment

I am assigning values to objects in a process. I would like the values to end up being normally distributed with variance one. For this I standardise them by subtracting their average from each and ...
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Coupling between mean and standard-deviation

For a one-sided distribution such as Poisson or the exponential distribution (but not specifically those particular one-sided distributions), $$ p_x(\alpha) = 0 \qquad \forall \alpha<0 $$ is there ...
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Why is standard deviation calculated differently for finding Z scores and confidence intervals?

Suppose that as a personnel director, you want to test the perception of fairness of two methods of performance evaluation. 63 of 78 employees rated Method 1 as fair. 49 of 82 rated Method 2 as fair. ...
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What's so special about the number '2' in the standard deviation?

If I'm not mistaking standard deviation is defined as $\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \mu)^2}$ .You could rewrite this as $\sigma = (\frac{1}{N} \sum_{i=1}^N |x_i - \mu|^c)^\frac{1}{c}$...
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Why do we calculate variance if standard deviation serves the ends well?

I don't understand why we even care for square units. How does it make sense that if you take the squared difference of each data set and mean, then divided it by $n-1$ gives us a measure of spread? ...
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Finding Mean And Standard Deviation Given the Values for the Top 25% and Bottom 25%

I essentially have a situation where heights are normally distributed and I'm given the top 25% of heights and bottom 25% of heights. How would I find the mean and stdev? This is my first week of ...
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If 2 grp have different SD but same mean, how do I know their SD given their combined SD and mean?

Known that entry IQ of a school is 138 (assume all eligible student will be accepted) female has lower SD than male the proportion of the school is 2/5 female, 3/5 male IQ are normally distributed ...
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Non-standardised central limit theorem

Let $(X_n)_{n}$ be a sequence of i.i.d. real random variables with mean $\mu \in \mathbb{R}$ and variance $\sigma^2 > 0$. Let $S_n = X_1 + ... + X_n$. The usual central limit theorem ensures that $\...
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Uncertainty on a poisson distributed probability?

I know that the standard deviation is the square root of the mean if the random variable is poisson distributed, but do you assign that to the probability of a certain event? Let's say that for the ...
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What is the equation for the standard deviation of the set of all odd integers?

I have a set containing all of the odd integers in the integer set. It is denoted by $O=\{2n+1\mid n\in \mathbb{Z}\}$. I want to write an equation that equals the standard deviation of the set. If I ...
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Why do we approximate sample stdev using sample stdev / sqrt(n) when population stdev is unknown? [closed]

In this stackoverflow stdev estimation question, we are discussing about when to use z-distribution and t-distribution. Now, I'm getting confused here why are we taking the indirect & apparently ...
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Need help with understanding this math part from the book "An Abundance Of Katherines" by John Green

I am reading the book "An Abundance Of Katherines" by John Green. There is a lot of math stuff in it which I am unable to comprehend. Somebody help me out in this regard. Here the ...
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Let $X∼N(\mu_1,\sigma_1^2)$ and $Y∼N(\mu_2,\sigma_2^2)$ be two independent normal variables. find $x$ so $\Phi(x)=P(X_1<4X_2)$.

Let $X\sim N(\mu_1,\sigma_1^2)$ and $Y\sim N(\mu_2,\sigma_2^2)$ be two independent normal variables. calculate $x$ so $\Phi(x)=P(X_1<4X_2)$. I know that this question should be solved by ...
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The production line in the dairy stops for every 1 in a 100 cartons as the cartons cannot hold the amount of milk the machine is trying to put in them [closed]

A dairy produces cartons of milk with a mean capacity of 1 litre. Cartons of milk containing less than 960 ml are sold at a reduced price. The volume of milk in the carton is normally distributed with ...
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Normal distribution: Find the range of masses, symmetrical about the mean, such that 50% of the eggs are within this range.

A particular breed of hen produces eggs with a mean mass of $60$ grams and a standard deviation of $4$ grams and mass is found to be normally distributed. Eggs are classified as small if their mass is ...
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Normal distribution with shortened units

I was solving an exam problem: Website's number of clicks per month is a random variable with normal distribution, where the mean is 12 and the variance is 2 (both in millions). Calculate the ...
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1 vote
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Estimating volatility of a geometric Brownian motion at different sample rates

I have troubles estimating volatility (= standard deviation of log returns) when the data is re-sampled at different sample frequencies. Problem I have generated a time series data using a geometric ...
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How can I compute the conditional mean, given a standard deviation?

Suppose that I have knowledge of a population's mean and standard deviation. Then, new information is provided to constrain the draw of the next sample to be at least a certain value: the value is <...
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Is there a relationship between the retrieved spectrum width with the ratio between actual spectrum width and resolution?

I have a time domain data which when converted to frequency domain gives a Gaussian spectrum. If I have limited number of samples in time domain, my frequency domain resolution is bad. In that case, ...
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Difference between true standard deviation and population standard deviation

What exactly is the difference between the two? Is it true that if you have been given the true standard deviation, you have to use the Z-score and if you have been given sample standard deviation, ...
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The question of standard deviation in gap statistics

From the paper of gap statistics, $\text { we estimate } E_{n}^{*}\left\{\log \left(W_{k}\right)\right\} \text { by an average of } B \text { copies } \log \left(W_{k}^{*}\right)$, $sd(k)$ is the ...
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Find the standard deviation $\sigma $ of a Normal Distribution [closed]

The question is: Consider a normal distribution curve where the middle $70$ % of the area under the curve lies above the interval $( 8 , 20 )$. Use this information to find the mean and the standard ...
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special discrete random variables

The bank issued loans to two groups of borrowers: 180 borrowers in the first group and 70 in the second. It is known that borrowers from the first group repay the loan with a probability of 0.93, and ...
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is 2 groups have the same mean but a different standard deviations will the combined SD be in between the individual SD's?

As spoken in the above question, If I have two groups of known Standard Deviations and the same Mean when combined the mean will remain the same but is the standard deviation guaranteed to be between ...
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Summation of variations $\sigma^2$ of several independent random signals

Is it possible to prove that for several independent random signals (variables) their variations $\sigma^2$ are added? I found it here, but without proof.
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