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.

learn more… | top users | synonyms

0
votes
0answers
17 views

Standart deviation of a hypergeometric distribution

So, here is the problem, I have 40 green marbles and 60 red marbles. 20 marbles are taken without replacement. Determine the standard deviation of the number of green marbles taken. I used the ...
0
votes
0answers
15 views

Choosing between several methods to replace bad or missing data.

We are doing some quality control on data coming in from stations all over the world. Part of the quality control involves testing the data on several different things like plausibility, etc. If a ...
0
votes
0answers
24 views

Normalize graphs to a specific heigh

I have the below graph generated in excel And I want to normalize the 4 curves to have the same height. I want their peaks to be at the same height as the "Average" curve, after normalization. Can ...
0
votes
0answers
86 views

Calculate new variance when sample size increases

Suppose I have 10,000 data points with the following statistics: Sample mean: 7 Sample variance: 4.2 (and hence standard deviation 2.05) Population mean is also 7. Now if I increase the sample ...
0
votes
1answer
29 views

Will the mean equal the standard deviation

In my problem, there are three classes that have each taken a test and in these classes, there are 99 students. Class A had 1 student who scored a 1, 1 students who scored a 99, and 97 students who ...
1
vote
1answer
48 views

Standard deviation of flipping coins

My question deals with flipping a coin. I figured out that in one session of flipping a coin 400 times, the standard deviation for a 95% confidence interval is 20. I understand this to mean that (95% ...
1
vote
0answers
15 views

How to find the +/- error of a radial average?

I have a set of directions in degrees in which I want to find the average and the distribution error. At the end of the day, I want to say something like: "Given these 100 directions, the average is ...
0
votes
1answer
21 views

How to find a data value using only standard deviation?

I have a homework problem with the following data values: x, 17, 24, 13, 21. I need to find x, but I do not have the mean. I only have the standard deviation, which is square root of 14, or 3.745. How ...
1
vote
3answers
85 views

Difference between these two standard deviation formulas?

Today I started reading statistics and I came across these two S.D formulas: $$\sqrt{\frac 1 n \sum (X - \overline X)^2} \textrm{ and } \sqrt{\frac 1 {n-1}\sum (X - \overline X)^2}$$ What is the ...
0
votes
0answers
93 views

Approach to build multivariate ranking system?

I have data of various sellers on ecommerce platform. I am trying to compute seller ranking score based on various features, such as 1] Order fulfillment rates [numeric] 2] Order cancel rate [...
0
votes
1answer
28 views

Standard Deviation Adjustment

Is it true that to change the mean and stdev of a normal distribution (with mean 0 and stdev 1), all one has to do is to multiply the current PDF by the new stdev and add the mean? I.e. I have N(0,1),...
0
votes
0answers
36 views

Find the time offset using standard deviation

maths is not my strong point so I am trying to make sense of this. Basically I have a thermal camera that takes pictures many times a second. This camera has an internal clock that records a time ...
1
vote
0answers
23 views

How to compare standard deviations of different sample sizes

I am interested in estimating the value of an unknown, random variable, X. X changes over time. So, X = X(t) = Xt At specific time intervals, I estimate the value of Xt using 7 different methods. Some ...
0
votes
1answer
911 views

How to calculate two populations combined mean and standard deviation.

I'm trying to solve following type of combined date given question. Imagined that there's two factories. They are X and Y. "X" factory has 10 workers and "Y" has 20 workers. These two factory's ...
1
vote
1answer
32 views

Standard deviation misunderstanding

Here is a question that I stumbled upon (and the solution to it, my reasoning follows after the image): I answered "The two quantities are equal". My reasoning was as follows: the question mentions ...
3
votes
1answer
68 views

Correct Intuition? Standard Deviation and distance in $n$ dimensional space.

Basic Question Is there an intuitive explanation of standard deviation in terms of Euclidean distance in $n$ dimensional space? Longer Version of Question To begin a more detailed sketch of my ...
0
votes
0answers
13 views

Variation test for Poisson distribution

I have two groups of data following Poisson distribution. I want to check if the two groups have the same variation (or if variation of one group is larger). I know F-test can be used to do this, but ...
1
vote
1answer
100 views

Standard deviation of the product of gaussians

What is the standard deviation of the product of two random variables that each have Gaussian Distributions? I don't even know where to begin on this problem.
0
votes
2answers
51 views

Normal distribution with standard deviation = I

Suppose a vector $\epsilon \in \mathbb R^d$ is a random vector drawn from the isotropic normal distribution: $\epsilon$ ~ $\mathcal N (0, I)$ [As in Eq. 1.34 here.] I suppose ...
0
votes
2answers
61 views

How does the formula for standard deviation result in the normal distribution

Trying to understand this is in a high school level. I understand that the how $\frac {\Sigma|x-\bar x|}{n}$ calculates the mean of the distances of each score to the mean. I use this idea to map ...
1
vote
1answer
50 views

3-sigma approximation

I am making a system involving a sensor who has to be really precise. I found on their datasheet a diagram that shows the typical performance of the sensor. There's the mean value, the +3 sigma, ...
0
votes
1answer
145 views

Calculating cumulative error in distribution of elements

I am dealing with a real life situation where I have a distribution of 12 unique elements that can be permutated in any way possible (so 12! = 479,001,600 possible permutations). The index position ...
0
votes
1answer
31 views

By how much does the mean and standard deviation change over a certain amount?

The monthly profit of a small convenience store is a random variable with mean μ = 100 000 and standard deviation σ = 6 000. If we define Y to be the profit per year, assume that the monthly profits ...
3
votes
1answer
62 views

How many points necessary for standard deviation?

First off, I'm not a mathematician, and never took statistics in college, what I know about standard deviation I've learned in the past few weeks, so be gentle... I'm working on a piece of software ...
0
votes
1answer
16 views

How to choose the degree of freedom when calculating the variance var(X)?

I have seen in the text books that sometimes while calculating the Variance of a set of numbers $Var(X)$ = $\sum_{i}^{n} \frac {(x_{i}-\mu)^2}{n}$ also $Var(X)$ = $\sum_{i}^{n} \frac {(x_{i}-\mu)^...
0
votes
0answers
101 views

Variance decomposition of double sum

This question is about the variance decomposition of a double sum. For a single sum, it is well known that: $Var(\sum_{i}^{N}a_{i}X_{i})=\sum_{i,j=1}^{N}a_{i}a_{j}Cov(X_{i},X_{j})=\sum_{i}^{N}a_{i}^{...
3
votes
1answer
61 views

Sample standard deviation

Give a set of 3 integers between 1 and 9 that would give a) the smallest value and b) the largest value of s (sample standard deviation) and find the value of s: i)if repeats are allowed and ii)if no ...
0
votes
2answers
29 views

Finding standard deviation given joint probabilities

I'm trying to find the standard deviation of $Z = X + Y$ given the following table: I'm getting $E[Z^2] = 36.31$ and $E[Z] = 5.45$, giving me a variance of $Var[X] = 36.31 - (5.45)^2 = 6.6075$ ...
-1
votes
1answer
52 views

Probability distribution; what is probability that i wont spend more than 75% of the customers

Very simple question but I am kinda stuck. Suppose that evidence in sales data suggests that average amount spent by a customer in a store averages 35.60 with a standard deviation of 16.4. A sample ...
1
vote
1answer
38 views

Definition of standard deviation and $l_2$

If we denote the mean as $\mu$, then the standard deviation is: $$\sigma\equiv\left(\sum_{x\in X}{p(x)(x-\mu)^2}\right)^\frac{1}{2}$$ In other words, $\sigma$ is the average $l_2$ distance from $\mu$. ...
1
vote
1answer
81 views

How to find the minimum of $f(a_1, b_1, \ldots , a_m, b_m) = \sum_{j=1}^{n} (y_j - \sum_{k=1}^{m} a_kx_j^{b_k})^2$?

$$f(a_1, b_1, \ldots , a_m, b_m) = \sum_{j=1}^{n} (y_j - \sum_{k=1}^m a_kx_j^{b_k})^2$$ $$2m < n$$ $x$ and $y$ are constants, and $a$ and $b$ are variables to find. I took deviation out of it and ...
1
vote
1answer
30 views

Isolate Sigma and FWHM from gaussian

I have the Gaussian: $a e^{-b^2 (x-c)^2}$ And need to isolate the Sigma and FWHM from it. I believe that $b = \frac{1}{\sigma^2}$ and $FWHM = 2.354(\sigma/2)$ However, I need to program this ...
-1
votes
1answer
43 views

Standard Deviation comparison

Currently i am working on my master thesis. I performed a research of the weather on sales. Different weather types are included in the model such as sunshine duration, duration of rainfall and level ...
1
vote
0answers
33 views

Statistics,standard deviation,spread,gemoetric meaning

What are the geometrical interpretations/meanings of these statistical quantities: mean, standard deviation and spread?
1
vote
1answer
173 views

How to perform mathematical operations using mean and standard deviation.

It's given that a particular parameter, say base-time $T_b$ follows a lognormal distribution with the mean of $10$ years and the standard deviation of $5$ years. Now, how do I estimate the value for ...
1
vote
0answers
53 views

Portfolio sd, covariance over different time periods

So we are trying to forecasted portfolio return and deviation of a historic set of investments, we have different lengths of data for different investments. My boss calculated the covariance using the ...
0
votes
0answers
91 views

Converting one normal distribution to another

I have a long data similar to this; between 15 and 25 consider its mean as m and calculated standard deviation using this formula. I assumed the above data as a normally distributed data and can ...
1
vote
1answer
19 views

studying set I of population

let x be the mean and € the standard deviation of the statistics ×1,,,,,,, xn. let I=(x-3€, x+3×€) and the number of items not in I is k. prove that n greater or equal to 9k. prove that the percentage ...
0
votes
0answers
42 views

How to reduce the standard deviation from $P$ where $P$ involves a random integer uniformly distributed in $\left[ 0,100\right]$

I have a probability $P$ derived from: - A random integer $A$ uniformly distributed on its range such that $A\in\left[0, 100\right]$ - An integer $K$ such that $K\in\Bbb N$ - A number $X$ such that $X\...
1
vote
2answers
428 views

why the standard deviation is not as the same as online calculator

I need to calculate the standard deviation for these numbrs: -12 -3 0 -13 8 -6 0 -22 -1 7 -7 1 -2 -13 -4 0 -6 -4 -10 3 I did everything, but still my answer is ...
2
votes
1answer
93 views

What to call & how to compute errors in a very asymmetric sample

Consider the following sample $\{1.25,1.5,1.75,2.0,2.25,2.5,2.75,10.\}$. Mean is $\mu=3.$, standard deviation is $\sigma\approx 2.69$. I am wondering how to compute and what to call error bars in the ...
1
vote
1answer
223 views

What is meant by statisticians when they talk about between population differences vs within population differences?

Suppose we have two populations of people in different parts of the world and we want to talk about the variation in heights between the two populations. As I understand it, statisticians are talking ...
1
vote
1answer
39 views

Statistics- Finding Probability

A local lawn service has determined the average time it takes to mow an average residential yard is thirty-five minutes. If mowing times are independent and constant, what is the probability it will ...
2
votes
2answers
116 views

A casino owner is concerned based on past experience that his dice show 6 too often

Currently I am trying to understand hypothesis testing, but I have a problem with the following question: A casino owner is concerned based on past experience that his dice show 6 too often. He makes ...
0
votes
1answer
28 views

Will calculating standard deviations from percentages give different results to claculating them from the raw data?

I'll start off by saying I am not a mathematician, nor have I studied maths for many years, so please keep the answers simple :) I am working with data that has a geographical context. So assume I ...
2
votes
1answer
35 views

How do I calculate if a line on a graph is generally far away from another line?

disclaimer: I'm (evidently) not a mathematician/statistician and a total n00b so if this question is too basic for the community let me know! Also excuse any misuse of terminology! Say I have two ...
3
votes
0answers
30 views

Removing slope from running times

First of all, & looking at the suggested question list, I hesitate at asking this basic question: Here goes. I'm trying to assess my fitness, and I need a bit of mathematical help. I do a little ...
3
votes
2answers
88 views

Calculating the sample standard deviation

I've been preparing for an exam tomorrow and was doing a past paper when it appears the mark scheme has an answer that I just cannot fathom. The exact question is to "find a 95% confidence interval ...
0
votes
0answers
54 views

Geometric Mean of Random Variables

I measure a series of $n$ objects [O_1, O_2, O_3, ..., O_n]. Because those measurements are quite hard to perform, I have quite a lot of measurement error and ...
2
votes
1answer
106 views

Standard distribution formulae trick

I am trying to understand the following question. The height of adult males is normally distributed with a mean of 172cm and standard deviation of 8cm. If 99% of adult males exceed a certain height, ...