suppose you calculate a mean of a population and you want to know how representative that mean is of a random?
956188
What you're looking for is the standard deviation.  If the data values are X and the mean is XBAR, then\n\nS.D. = sqrt{[SUM(X - XBAR)^2] / n}\n\nn is the number of data items, and SUM means to add up the squares of the differences between the data values and the mean.\n\nThe lower the standard deviation, the more tightly packed the data.  If the data is normally distributed, about 68% of the data will lie within one standard deviation of the mean, and 95% will be within two standard deviations.\n\n[Edit:  In light of the previous answers, I should add that the standard deviation is the square root of the variance.]
570786
First of all, if the population is normal, the distribution of sample means is normal regardless of sample size.  So I. is true.\n\nSecond, if the population is not normal, the distribution of sample means is approximately normal if the sample size is large.  So III. is also true.\n\nII. cannot be determined to be true unless we know what the population looks like.\n\nSo I would go with C.\n\nUPDATE: Apparently ghakh hasn't heard of the Central Limit Theorem.  You know, the "Fundamental Theorem of Statistics"?  In layman's terms, it states that if the sample size is large enough, then the sample means will be approximately normal if the sample size is large enough REGARDLESS OF WHAT THE POPULATION LOOKS LIKE!!!!!!  All you need is a finite variance, which for elementary statistics students is not something they need to be concerned with.\n\nMaybe you should take my statistics class, ghakh.  You might learn something!
276294
use the formula for confidence interval.. its found on most statistics book.. i would type the formula, but that wouldn't be helping you to be a better student..
614693
You can get an idea about what the distribution of the population is by looking at the five number summary (Minimum, 1st Quartile (Q1), Median (Q2), 3rd Quartile (Q3), Maximum).  For example, if the minimum and Q1 are close together, but Q3 and the maximum are far apart, then you can say that your data is right skewed, meaning that the outliers tend to be larger values.\n\nWith a sample, it is hard to say whether the population is normally distributed or any other specific distribution with a sample alone.  You need to know something about the population to make a statement like that.
871703
Sorry, if the result can be greater than 1 then you ain't estimating a proportion.  For proportions each unit in the sample gives you either 0 or 1 as a result.\n\nYou need to swith to the general case where you calculate the standard deviation from the sum of squared differences from the mean, etc. PQ/n or whatever cannot be applied.
911284
You would use monte Carlo simulation when you need to find the distribution of a variable, and this depends on other variables which are random, especially when the interact in a complicated way.\n\nRather than trying to work out an answer, you just run the model using lots of different random numbers as inputs.  The outputs should approximate your answer if you have enough inputs.\n\nThese can be checked by using solvable cases.  I.e. consider the average value when you through a dice =(1+2+3+4+5+6)/6=3.5\n\nYou could also attempt to answer this by Monte Carlo methods by throwing a dice lots of times and taking the average of your results.  If you make enough throws the answer should be close enough for all practical purposes.
124804
For an uncertainty x of 0.01 (which your 99% accuracy would be) you need 1/x^2 samples which would be 10000.  This is true for a large population (>>10000).  I believe you still need that many for 20000 population but am only 99% sure.\nSource: Best recollection of a stat course 50 years ago.
957375
Sample means you only obtain a part of the data.  Population means you obtain all of it.  When calculating sample standard deviation you divide by one less that the number in your sample; population S.D., divide by the full number in the population.
905827
If a random variable has a standard deviation of s and you take N samples, then the standard deviation of the sample mean is s/sqrt(N).\n\nIn your case you assume that the standard deviation of the random variable is close to 50 because you have such a huge number of samples. Now if you turn around and only look at 30 samples then the standard deviation will be\n50/sqrt(30).
790907
b is the most convincing.\n\n90 is the value farthest from the mean, and a small sample variance indicates that it's unlikely that you just somehow ended up with an unusually high (or low) population.
1156399
This is a good question even for a statistician.\nThe problem is your set is small and I do not know what the deviation between samples is, however the repeatability and reproducibility information can bind the window \nthrough which the third value will fall through or perhaps even remain in.  \n\nLet me know.
303094
OK.  From any given population, you can take many, many different samples of size n.  For each of those samples, you can find the mean.  So if you take 1000 samples of size 50,  Then you would have 1000 sample means.  Now each of those sample means are probably going to be different from the overall population mean, since samples are going to look different from the population.  Also, each of the 1000 sample means are going to look different from each other because the mean is coming from different samples.\n\nSo if I were to draw a histogram (hopefully you know what that is; it is a bar graph that you can use to look at the distribution of numerical data).  Anyway, if I were to draw a histogram of my 1000 sample means,  You should notice the following three things...\n\n1.  The center of your histogram should be the same as you population mean (so if the mean of the population is 20, then the histogram of my 1000 sample means should center around 20).\n\n2.  As the sample size gets larger, the spread of the histogram should get smaller (so the spread of the means of samples of size 50 would be smaller than for the means of samples of size 25).  This is because with larger samples, you would have more information about the population, and thus you should be able to get closer to the population mean.\n\n3.  As the sample size gets larger, the shape of the histogram will look more and more like a normal curve.\n\nThis is because of the Central Limit Theorem, that states that if you take a sample of size n from any population with a finite variance, the distribution of the mean of the sample would get closer and closer to a normal curve as n gets larger.  The mean of the normal would be the same as the population mean, and the standard deviation of the normal (usually called the standard error) would  be the standard deviation of the population divided by the square root of n.  Notice that as n gets larger, the standard error gets smaller, just as described before.  So typically you can approximate these histrgrams with a normal curve if n > 25.\n\nThis phenomenon is hard to describe in words alone.  Looking at pictures of these histograms that I described would help you understand it better.
192872
You must look at the formula for standard deviation of the sample distribution of (I'm thinking) binomial distributions. The proportion "p" is a parameter of the formula. You should check it out but, if I remember correctly, it's:\ns.d. of the sample distribution = sqrt[p*(p-1)/n]
729266
Yes.  This would require the use of a t confidence interval.  That is because the sample is small, the population is normal, and the population standard deviation is unknown.  You would have to compute the mean and the standard deviation of the six values to determine the confidence limits.\n\nedit: BTW, the mean is 81.98 and the standard deviation is 4.18.  The confidence interval I get is (77.18, 86.87)
73353
Statistics can be realied upon to a certain degree, but it really depends on where the stats are coming from, are they coming from a realiable source, or from a friend of a friend of a friend?\nMost statistics are made up from a small survey of people, for example viewers who watched a particular show. The actual number of people that watched the show may be 20,000, but these are only the people who have the equiptment attached to their tv set to show what they watched and when so to get a realistic figure they may count each person as 1,000 to get a more realistic figure. In actual fact everyone else may have been watching something else.
488365
Try again Paul C.  The population doesn't need to look normal.\n\nThis all comes down to the Central Limit Theorem.  Let's assume that I take many samples of size 1004 from the population.  Well, each sample will have a percentage that is different from the population percent, because samples are going to look different from the population.  Also, each sample is going to look different from each other, because they are different samples.  If we were to draw a graph that looked at the "behavior" of these many samples, we would notice the following:\n\n1.  If I were to average out all of these sample percents, I would get the population percent.  Hopefully you can see why this would happen.  Sample percents will be around the population percent, but just be off by a little bit.\n\n2.  If I were to look at the spread of the percents, the spread would be smaller as bigger samples were taken.  In other words, if I had taken samples of size 500, the sample percents would be more spread out than for samples of size 1004.  That is because if were take larger samples, then we have more information about the population, so we should expect to get closer to the population percent.\n\n3.  As I take larger and larger samples, the shape of the graph of sample percents would look more and more like a normal curve.  A normal curve is shaped like a bell, where the middle of the bell is were the population percent is.\n\nSo Paul C, it doesn't matter that the population doen't look normal; all we need is a sample that is large enough.\n\nNow the margin of error on polls is typically going to be\n\n2*sqrt(p(1-p)/n))*100%\n\nwhere p is the sample proportion (the sample percent divided by 100%) and n is the sample size.  It can be shown that this margin of error would be at its largest if p = 0.5, so the largest the margin of error would be in this case would be\n\n2*sqrt(0.5*0.5/1004)*100% = 3.2%\n\nThis is typically associated with 95% confidence.  This basically means that if I were again to take many, many samples of size 1004,  95% of the sample percents would be within a margin of error away from the true population percent.\n\nThis of course depends on the sample that is taken.  The online polls that you see would not be good estimates for the population percent.  Below I have a link to a story that MSNBC has on each of its online polls.  The title is "How 1,000 people can be more representative than 200,000."  I think that it is a very good explaination of this topic.
111022
7\n\norder them; if you have odd number of entries, take the middle one; if even - take average of two middle ones.\n\n\n\nand it's a statistics question