Standard deviation Definition and 271 Threads

Homework Statement Let x_{1},...,x_{n} be n observations. If y_{1},...,y_{n} is another set of observations s.t. y_{i}=ax_{i}+b , prove that s_{y}=|a|s_{x} . The Attempt at a Solution Attempt at a proof: Since \bar{y}=a\bar{x} +b then \bar{x}=(\bar{y}-b)/a and...

Hello, I'm doing some nonlinear regression fitting, and I have a set of data with n data points and I am fitting the data to a model which contains 3 parameters. I can get a confidence interval from the program I'm using for each parameter, but how can I calculate the standard deviation for...

Hello all This is not homework, i work in engineering. I have some data in a table, there are 3 columns and 5 rows. The data relates to how high or low one rail is to the other. The data was collected across 3 days. At each 7m intervals the height of the right hand rail was...

The length of time, t minutes, taken to do the crossword in a certain newspaper was observed on 12 occasions. The results are summarised below. Σ(t − 35) = −15 Σ(t − 35)^2 = 82.23 Calculate the mean and standard deviation of these times taken to do the crossword. My real problem is finding out...

I missed the lesson on this and i can't figure out how to do this question with the data given. Homework Statement A class of 20 students takes a test. The score, x , for each student was recorded by the teacher. The results of summarised by: ∑(x-10) = 208 and ∑(x-10)² = 2716 i) calculate...

Homework Statement i'm given the population mean and standard deviation. A new batch comes in and given a random sample. the question asks do i believe the new batch has a different mean from the overall average? Homework Equations The Attempt at a Solution so i got the mean and...

Hi, Can anyone point me to a reference for the statistical properties of the sample standard deviation of a sequence of identically distributed normal random variables subject to some form of serial correlation? Thanks, rhz

Hello All, I am trying to figure out how to find the standard deviation or error in sets of data. So let's say I have sets x1, x2, x3 and x4 with various values and I found the average and standard deviations for it. Now I have to take the averages, let's say a1, a2, a3, a4, and normalize...

Hi Say I have a linear problem Mp = d, where d is our data, p our parameters and M our "observation matrix" (see http://en.wikipedia.org/wiki/Inverse_problem#Linear_inverse_problems). So what we are dealing with is an overdetermined problem. Now, I have read an example where we have a...

Not sure if this is where this question belongs because the course I am doing is predominately calculus based (Applied Physics, University level) but we have a small statistics component for obvious reasons. Any who, sorry if it's in the wrong spot. Homework Statement Intravenous fluid bags...

Hi If I have measured the resonance frequency of three sets of resonators and calculated the mean, variance and standard deviation for each set. How do I add the three variances and standard deviations to get an overall variance and standard deviation? Well, I know that the standard...

I am working with some wind speed data and need to work out the standard deviation of the magnitude of the horizontal wind. Unfortunately the only information I have is the standard deviation for the streamwise and cross-stream components of the wind (which are orthogonal). Is it possible to...

Homework Statement Suppose that the systolic blood pressure of 20 year old females is normally distributed with mean 120 and standard deviation 15. a.) What proportion of 20 year old females will have readings between 115 and 125? b.) If you selected a sample of 64 people from this...

Homework Statement Write a C++ program that accepts 10 floating-point values from a user and determines and displays the average and the standard deviation. All values more than four standard deviations away from the average should be dropped and then the new average and standard deviation...

Consider the Uniform distribution (continuous) U(-1,1) which has p.d.f. f(x) = 1/2 for -1 < x < 1 and 0 otherwise. I have calculated the Fourier transform using the characteristic function and got fhat(epsilon)= sin(epsilon)/epsilon How do I calculate the standard deviation of this...

Homework Statement The average monthly expense of a certain family during 11 months is 4000 shekels, with a standard deviation of 100 shekels. Afterwards they added to the calculations the family's expense at the 12th month, and they found the average remained unchanged. A) What was...

Homework Statement The grades distribution in class is 10, 8, 8, 7, 7, 7, 6, 6, 4 What's the standard deviation? The Attempt at a Solution I found the average is 7 (which is true) and used the formula for standard deviation. I checked it twice on the calculator but I'm still...

Let's say I have a big, 50-sided die, with values ranging from 1-50. I want to find the exact standard deviation of the dice roll by hand. I would like to avoid subtracting the mean from each possible value, if at all possible. How do I do that?

Suppose the men in a country have a mean life span of 79 with a standard deviation of 8. And the women in the country have a mean life span of 83 and also a standard deviation of 8. Furthermore, suppose the life spans are normally distributed. What is the mean life span of the entire...

How to convert error to standard deviation? I explain my simple question: I have a program that requests the standard deviation of a physical measurement. But I only have the error, let's say v=-3.445643 +- 1.5%. How do I make the conversion? Please

Homework Statement A high jumper knows from experience that she can clear a height of at least 1.78m once in 5 attempts. She also knows that she can clear a height of at least 1.65m on 7 out of 10 attempts. Find to 3 dp the mean and standard deviation of the heights the jumper can reach...

Homework Statement Carbon rods with a nominal diamter of 1.5cm, it is only acceptable within the limits of 1.495 to 1.505cm. the actual diamter normaly distributed with a mean of 1.501cm with standard deviation of 0.003cm. what will be the percentage of the rods which are rejected if 1-...

Homework Statement i have a few results of measurements, with different measurement uncertainty: L=5\pm0,2, L=5,1\pm0,1,L=5,2\pm0,3,L=5,3\pm0,1,L=5,4\pm0,2 and how can i count standard deviation and final result of measurement with uncertainty? The Attempt at a Solution i counted arithmetic...

Hello all, I am trying to figure out the following question with no luck: I have a box of resistors, mean 100 ohms and SD of 20 ohms. I form a subgroup of these resistors with mean of 100 ohms and SD of 5 ohms. Find the standard deviation of the remaining sample. The question does not...

Let X and Y be the per dollar return of 2 stocks. Suppose that both have an expected return of 0.05, both have a variance of 0.0009 and covariance(X,Y)= -0.001. Suppose that you invest $50 in the stock with return X and $100 in the stock having return Y 1) Calculate the expected return of...

Can somebody explain to me why we have to square the variances when calculating the deviation and then finding the square root(whc is suppose to reverse the squaring) ,it doesn't make sense to me

I have a question of testing of hypothesis about mean, the population S/d is not given rather it says "a client gave Quality Associates a sample of 800 observations taken during a time in which that client’s process was operating satisfactorily. The sample standard deviation for these data was...

Hi all, I've done a regression and have the Standard Error of the X co-efficient (i.e. the slope). How do I change this figure to the standard deviation? Is the formula STD DEV = (STD ERROR)/(degrees of freedom)^0.5 Where degrees of freedom = N - number of X coefficients. ...

#of nickels needed when only standard deviation is mentioned A previous study of nickels showed that the the standard deviation of the weight of nickels is 150 milligrams. A coin counter manufacturer wishes to find the 98% confidence interval for the average weight of a nickel. How many...

I'm doing a lab report, but I don't need help for it. I just need the standard deviation in g. I need to compute the theoretical value for centripetal force together with its uncertainty for my circular motion experiment. That is, since my mass was measured to be 0.208536kg, standard...

Homework Statement The distribution of a drugs among addicts with autoimmune disorder is N(6.9, 16.81). What is the probability that one of these addicts enters your office and reports taking 16 drugs or more? The Attempt at a Solution z = (16-6.9)/4.1 = 2.21 P(z >16) = 0.014 from...

Homework Statement The scores of one class on the Unite 2 mathematics test are shown in the table below. Find the population standard deviation of these scores, to the nearest tenth. Unit 2 Mathematics Test Score - Number of people 96 - 1 92 - 2 84 - 5 80 - 3 76 - 6 72 - 3 68...

Hi, I'm having a little trouble with this question: Among entering students at a certain college, the men averaged 650 on the Math SAT, and their SD was 125. The women averaged 600, but had the same SD of 125. There were 500 men in he class, and 500 women. Q) For the men and the women...

Homework Statement A sales contract between a manufacturer and a buyer requires 20 towels to be subjected to a water absorption test. If no more than 2 towels fails the test, the batch is accepted. If 2 or 3 towels fail the test, an additional 20 towels are tested. The batch is then accepted...

Let's say I monitors my local aquifer (Edwards) using well J-17 over the past 8 summers (not counting this summer). I found that the mean water level/day is 680 ft above sea level, with a standard deviation of 30. Assuming a normal distribution, how do I find the probability that the aquifer...

Homework Statement I have two sets of data, each with 30 distances and 30 results, I have the mean, median, mode, range etc, I have drawn histograms and cumulative frequency curves, got the IRQ for both sets of data. Now I need to compare the data using standard deviations and also find...

What does this mean? Average? Sum?

OK I was going to post this in homework, but it's not homework (left school a long time ago ;)) Anyway when I was at school I did not do stats I did mechanics instead (you had a choice). However all the people doing stats were always on about the the SD, which was a bit annoying cos I...

I would like to understand the theory behind the standard deviation formula. The way it was explained to me, you have to subtract each value from the mean and square it to avoid the negatives canceling out the positives. After multiplying and dividing by the correct frequencies, we have to...

[b]1. A voltmeter is used to measure a known voltage of 100V. Forty percent of the readings are within 0.5V of true value. How do I figure out the standard deviation of the voltmeter, and how do I figure out the probability of an error of 0.75V? [b]2. I am trying to figure this problem...

Homework Statement Sally, Bob and Charlie each measure the period of the same pendulum to determine the acceleration of gravity, g. The lab instructions say that you should determine the period by timing the time of 100 swings (complete cycles) of the pendulum. Sally is the first to do the...

Homework Statement Students measured an object 5 times, and got the results 11,25 cm, 11,20 cm, 11,22 cm, 11,18 cm i 11,25 cm. The height of this object is: A. h = (11,22 ± 0,03) cm B. h = (11,22 ± 0,04) cm C. h = (11,25 ± 0,07) cm D. h = (11,25 ± 0,03) cm Homework Equations Standard...

Homework Statement Homework Statement Hello everyone! I have been having trouble with cumulative frequency graphs in excel for some time now. I wonder how you make the "bell graph" or cumulative frequency graphs or standard deviation graphs in microsoft excel. I have excel for mac. I...

Given an imaginary, mechanical chimpanzee that never wears out nor sleeps nor relents. Who is compelled to type constantly through eternity into an endless text file using a US standard keyboard... as fast as he can. That this monkey knows simply that he must hit only character keys and only one...

By definition standard deviation has divisor 'N' . But in Microsoft Excel the "STDEV" function gives 'N-1' as divisor. This may not be major issue to many of the people. But the command "STDEV" makes many users feel that this is standard deviation, i.e. it has divisor 'N'. Misleading...is...

The problem is to find a closed form for the expectation (mu) and standard deviation (sigma) of the probability density function underneath (Maple notation): f(t) = a*exp(a*t)*BesselK(0, 2*sqrt(exp(a*t)))/BesselK(1, 2) I was able to find an expression for mu:: mu =...

i would post this in the chem section but more people view this one.. im having a quiz on standard deviation in chemistry lab onf riday, and I am not sure AT ALL how to do this. i tried asking the teacher but he's not to good at explaining. and i tried lookinga t the difficult to understand...

Hello! Quick question: Is this valid: (\frac{standard \left \left deviation}{average} * 100)? The standard deviation is just a measure of the spread of the data from the average, so by doing the above, is it retaining its 'representation' as a measure of spread, just as a percentage of the...

I need to calculate the average time of an event, and I'd like to calculate standard deviation as well. The problem is - there is no such thing as negative time - zero is a boundary - so how does it make sense if the average is 4000us (microseconds) and the stdev is 5000us? Is there a...

Homework Statement http://img338.imageshack.us/img338/5064/picture1nk.png 2. The attempt at a solution I know the area for -1.5 is .0668. I also know that the area of the positive half of the curve is .5000. I don't know how to figure out what the other blue piece is or how much the white...