Standard deviation Definition and 271 Threads

I need to prove that $$std(x+c) = std(x)$$ I have been trying to use the properties of the mean such as $$mean(x+c) = mean(x) + c$$ I am confused on the following property of the mean, is this statement correct? $$\sum\limits_{i=1}^{i=N}(x_i - mean(\{x\}))^2 = mean(\{x\}) \\$$ If that is...

my question is on part ii, my range ( as shown in the photo), is between 4.52 and 16.28, so my working would be (6+10+4+4)/(6+10+4+4+1) X100% ... the answer given is 72% which is differnt form my answer? which part of my working is wrong ?

What is the significance of the standard deviation (equal to the mean) in an exponential distribution? For example, as compared to the standard deviation in the normal distribution, which conforms to the '68-95-99.7' rule? thanks

If thermodynamic temperature can be interpreted as the average kinetic energy in a system, is there a quantity defined as the standard deviation? For example, let's say you poured some hot water into a cup of cold water. The instant you poured it the standard deviation of the system would be...

Homework Statement Here is a slide in my notes: I am kind of confused about mean and standard deviation. So in my notes it says X1 to Xn are independent measurements. Then it says each independent measurement has a mean μ. But how is this possible, if they are independent measurements (in...

In some textbooks ##\Delta \hat{x}## is called dispersion of coordinate ##\Delta \hat{x}=(\langle \hat{x^2} \rangle-\langle \hat{x} \rangle ^2)^{\frac{1}{2}}##. For me that is standard deviation. What do you think?

Homework Statement For a certain random variable X, P(X≤500)=.5 and P(X>650)=.0227, find σ. Homework Equations μ=expected value=mean Variance=∫(X-μ)2fx(X)dx evaluated from -∞ to ∞ σ=√Variance The Attempt at a Solution I'm not sure what the relationships between the...

After filling out the table, I used it to finally calculate the standard deviation as 0.105. Just to make sure, I ran it through Microsoft Excel and got 0.942809042. I put two together and figured I'm doing something wrong after the xw column because Excel agrees that the mean is also 1.7...

Hello, PF! [My question pertains to a non-rigorous, undergraduate introductory Probability and Statistics course. I'm no math major, so please correct me if I've mishandled any terms or concepts as I try to express myself. I'm always eager to learn!] * * * In a discussion of the...

Hi,,,can u please explain me how to calculate standard deviation and standard error for a binomial distribution when you have several samples? For exapmple: I don't know the population size. I take a sample of 10 and check for a particular characteristic. Let's say number of successes for this...

I had this problem on a quiz and obviously got it wrong, I am confused about how to set this question up and what to solve for: In a large city, the average retail price of a pound of grapes is $1.79, with a standard deviation of 18 cents. Between what values must be the price of at least 15/16...

Hi guys, I hope someone is able to help me with this, I'm currently stuck on a problem. 1. I was given some data (in continuous, grouped form) regarding phone call times for a call center agent and asked to represent the data using the most accurate form of average. I initially calculated...

Hi guys, I hope someone is able to help, I'm currently stuck on a problem. I'm having trouble justifying which representation is more accurate for my data; either mean with standard deviation or median with IQR. I've calculated both averages for the my data, however I was advised by someone...

Homework Statement I have to calculate the standard deviation Homework Equations http://0.tqn.com/d/statistics/1/0/M/-/-/-/standarddev.GIF The Attempt at a Solution 0.64 0.4096 2.06 4.2436 0.16 0.0256 3.24 10.4976 1.74 3.0276 1.06 1.1236 4.04 16.3216 1.56 2.4336 1.3 1.69...

Homework Statement There are a set number of marbles in a bag; the marbles consist of two colors. We are given the mean number of marbles of color 1 in the bag, as well as color 1's standard deviation. We are then asked to find the mean and standard deviation of color 2.Homework Equations How...

Homework Statement People drink on average, 78L of beer per year with a standard deviation of 25L. at least what percentage of people would drink between 20 and 136L per year? The Attempt at a Solution I found the z-scores of both and they came up to be +/- 2.32. Compared these values to the...

Homework Statement Showing all your working, calculate the arithmetic mean and standard deviation of the number of days lost. Table shows man days lost to sickness.. Days lost: 1-3 4-6 7-9 10-12 13-15 Frequency 8 7 10 9 6 Homework Equations...

I have a one-dimensional set of data which I have attached an image of. This data is an intensity z, as a function of time, t. There are many data points over time with a large amount of scatter. However, if the data is binned over very short wavelengths we see that there is smooth variation...

Hello, I've been trying to find online where I could calculate my grade based off a college curve. So the average grade on the test was a 63. The RMS is 16. I got a 86. So what will my grade curve to? This is out of 50 people. Also, the professor curves to a 70 (I think).

I am measuring the thickness of many identically prepared objects. In order to obtain the most accurate value, I measure each object multiple times, in different locations, and average these values to get the average thickness of that object, along with the standard deviation. But I am really...

I was wondering if anyone could help me with calculating the standard deviation of the standard deviation. What I mean by this is say for example I roll a dice 100 times and then calculate the mean and standard deviation from the results I collected. The results are not going to be exact because...

Say we want to saw ten planks and we have two methods available - one is sawing them all at once, ensuring they're all exactly uniform length. The other method is sawing them individually. Either method has EV of 1m and a standard deviation of 0.005m. I want to find the standard deviation of...

How do I work out the standard deviation of a set of variables where the frequency changes by a certain factor each time, but where there is no limit on the number of variables? Let's just use "test scores" as an example because that's easy to understand. The average is 80; 1 in 5 people...

For a sample of size 5, if x1 - x̄ = -5, x2 - x̄ = 9, x3 - x̄ = -7, and x4 - x̄ = -2, then the sample standard deviation is: Choose one answer. a. 5.639 b. 6.782 c. None of the other answers are correct d. 6.305 e. 6.066 Please note that x̄ is x-bar (mean of sample). This...

Homework Statement I've still yet to learn Latex since I'm pretty good with words equation editor, so here's the question typed out in words. Homework Equations I really don't know what to do here. The Attempt at a Solution

I realize you can transform the data in many ways, but I really can't find a method to solve this particular scenario anywhere online: Suppose you are given the mean and standard deviation of a set of data. Further suppose you take away (get rid of) "x" elements in the original data set, and...

Hello people, I think the problem what I have is well known in experimental physics. Hope, somebody can helps me, thanks in advance. Here is: There is a source of neutrons with a flux of λ neutrons per minute, which you do not know and want to estimate. You open the detector for one minute...

I am en experimentalist and in most of my experiments I am interested in measuring the properties of distributions, i.e. the phenomenon I am measuring is stochastic and the parameters I am interested in are (in the simplest case) say the mean value and the width of the distribution (variance of...

Hi, I just solved a probability density function problem and the standard deviation is undefined.Does anyone know why it happens?It would help to develop my understanding.Thanks.

Hi everyone. I am currently in a club that prepares students for technical interviews for jobs such as investment banking, private equity and hedge funds. One of our mentors assigned us this question and to be honest I really do not have an idea how to approach it. I'm not sure if I am...

Homework Statement I teach a class of statistics with students who often do not have the types of calculators that can calculate standard deviation and who do not know how to program Excel, but do have access to the Internet. Googling "standard deviation calculator" on the Internet gives me...

I'm doing a practice problem for my upcoming midterm and am stuck on a question. 3. The number of hurricanes that occur in the caribbean during hurricane season is a random variable, where the mean number of hurricanes occurring is 8, or E(X) = 8, with a standard deviation of 2.83. (a) Find...

In Frank Attix's book on Radialogical Physics Equation 1.2a reads σ = √(E) ≈ √(μ) σ= standard deviation of a single random measurement Where E is the expecation value of a stochastic process which approaches μ (μ is the average of measured values) as the number of measured values...

Hello, If have the standard deviation of acceleration (acceleration > 0) for a car. I also have the standard deviation of deceleration (acceleration <0). With these two figures is there a way to get the a standard deviation of the acceleration (both positive and negative)? Thanks

Hello, I've been trying to find the answer to this question on the internet but no real luck so here goes: Imagine a signal My_signal which has two components, the actual signal A which is not constant over time and a noise component, we can call it N, where said noise component has a standard...

Hello, Just had a question regarding statistical analysis. I'm trying to calculate the average of 4 numbers from a data set of 6 numbers in excel without manually choosing to average only the 4 numbers. e.g. 85 20 32 45 27 3 (total mean = 35.3 desired mean = 31) 100 30 27 40 21 1...

Hello People, I'm and just somewhat confused about this topic. Lets say I have a sample set A with sample size= 101 mean =10 and sample stdv of 1 then sample set B with sample size= 100 Mean=15 with sample stdv of 2. If i add these two samples sets together I should get a new stdv that...

Homework Statement Just as the title suggests, although this is more to do with the formula. I know that for a sample, it implies it's a subset of a population. Why in the formula do you divide by n-1, whereas for calculating standard deviation for a population you divide by the total amount...

How is percentage uncertainty different from standard deviation ? I have five measurements and l calculated the average, standard deviation and variance. Do l need to calculate the percentage uncertainty ? Does percentage uncertainty give me any more information which the other values l...

I've done a decent amount of reading on the subject, and I used this method of course when reporting errors during lab experience I got as an undergraduate, but it was never quite fully explained to me why exactly we report a value +/- the standard deviation of the mean as our result. Why not...

I was wondering if someone could please help me understand a simple problem of error propagation going from multiple measurements with errors to an average incorporating these errors. I have looked on several error propagation webpages (e.g. UC physics or UMaryland physics) but have yet to find...

Hello, I am trying to calculate what the margin of error for the standard deviation would be if each data point has a margin of error E. The standard deviation (for 3 data points) is defined as σ = \sqrt{\frac{(x_{1}-μ)^{2}+(x_{2}-μ)^{2}+(x_{3}-μ)^{2}}{3}} Where μ =...

Hi, I am doing an undergraduate introductory statistics course and I'm trying to understand some basic concepts. I'm trying to understand why the sample size (n) affects the standard deviation of the sampling distribution of the mean (σ_{M}) I understand how a sample size affects the...

I've a set of tests, and for each test, they have different size. I'll show an example. Test1 size - Time(seconds) 100 - 10 100 - 23 100 - 17 200 - 37 200 - 42 200 - 47 300 - 53 300 - 53 300 - 53 For each test, I took the average. Average1 size - average 100 - 16...

I am trying to calculate the standard deviation of a group of data based on a 20 period sliding window. I have run into a bit of a problem in knowing how to deal with gaps up or down in the readings and was wondering what the correct method for compensating for this was.Below is an example of...

Hello folks, I've got a bit of a problem with estimating the overall error in measurement of a function which I have sampled at sixteen independent points and have calculated the associated error bar with each point. The problem is I'm not sure how to combine all the sixteen errors into a...

Can someone please explain how the standard deviation is relevant when we are talking Brownian motion? And why is statistics important when we want to understand the movement of a brownian particle?

Homework Statement There are 10 observations. (a) Suppose the IQR is 8. Is it possible that the standard deviation is 1? (b) Suppose the standard deviation is 8. Is it possible that the IQR is 1? Homework Equations IQR = R3 - R1 The Attempt at a Solution My argument is that (a)...

...I understand why it becomes more and more insignificant as the value of n increases, but what is the purpose of subtracting 1 from n in the sample population in the first place? Also, what is the purpose of squaring the result of x values minus the mean? I can do the problems. I'm just...

I've calculated the mean difference of my (normally distributed) data set. The mean difference is defined as: Now, I'm trying to calculate the "mean difference deviation" in order to generate a confidence interval for this quantity ( "95% of the differences in the set are greater than...