What does variance mean in statistics?
400910
"...the variance of a random variable is a measure of its statistical dispersion, indicating how far from the expected value its values typically are."\nhttp://en.wikipedia.org/wiki/Variance\n\nHere are some descriptions of how to calculate it:\nhttp://davidmlane.com/hyperstat/A16252.html\n\nCheers!
1062399
Mean is the average of the data.\nMedian is the middle number (if placed in ascending/descending order)\nMode is the number that appears the most.\n\nExamples:\n\nLet's say you are trying to discover the force of gravity by measuring the time it takes a car to roll down a ramp.  You know the length of the ramp and the angle of the ramp and therefore, need only a good approximation of the time that it takes for the car to go down the ramp (your number will be low do to friction).\n\nLet's say that these are the times that you got from 10 trials:\n\n\n9.3\n9.3\n9.9\n8.8\n9.5\n9.7\n15.4  (the car came off the track and was slowed down a lot)\n9.6\n8.9\n9.2\n\nThen you would have had a mean of 9.96\na median of  9.4 (line them up in ascending oder 8.9, 8.9, 9.2, 9.3, 9.3, 9.5, 9.6, 9.7, 9.9, 15.4 and since there is an even number of data points, take the mean of the 5th and 6th)\nand a mode of 9.3\n\nNow 15.4 is obviously a bad point.  Removing it we get:\na mean of about 9.7\na median of  9.3\nand a mode of 9.3\n\nSo only the mean really changes, this is because the mode and median are designed to get rid of "bad" data points.
351084
Most times statistics are used in psychology to measure whether the results of an experiment shows genuinely "significant" differences within the results, or whether all of the results fit within a single range.\n\nFor example, there have been studies which "appear" to show that boys' and girls' academic performance goes in non-synchronous waves.\n\nIf you measured the performance of all the pupils in a school in a certain year in a certain subject you could tell (using chi square, for example) whether the performance of the boys (as a group) was statistically different from the performance of the girls (as a group), or whether the performance of all the students in that year, in that subject, fell within the same "range".\n\nIf there is a significant difference you can use "standard deviations" as a measure of just how big the difference is.\n\n(I don't have any URLs on hand, but you can look up "statistical significance" and "standard deviations" online.)
256844
It allows you to compare different sets of data.\nSo one day when you have lots of different info, you can use these statistical calculations to make a decision that suits you.\n\nExample: Say you want to invest in stock. The mean gives you what you can expect to earn on the stock. The variance is a measure of how risky the stock is- the higher the variance, the more risky the stock. Usually a higher variance means you can expect a greater return(mean). The trick is to find the balance between maximising return while minimising risk.
411133
Eh?  Not sure what you're saying here.\n\nDo you mean "what is the correct way of talking about an average"?\n\nIn which case it is the average of the data (where we add up the results and divide by how many we had)\n\nAn average of an average would only make sense in the case where we are looking at the distribution of an average and then want to find the average result of that distribution.  If you want to go that way then....\n\nSuppose we have a population (eg people's heights) with mean 170cm and standard deviation 12cm.\n\nThe we take a sample of say, 50 values from that population (ie we measure the heights of 50 individuals)\nThen the we take an average (posh word: MEAN) of this sample.\n\nWe then take another sample of 50 values and get the mean of that sample.\n\nWe then take another sample of 50 values and get the mean of this sample.\n\netc.\n\nWe cacn then plot the frequencies of these means and get the distribution of these means.\n\nIt can be shown that it will have a normal distribution with mean 170cm (same as the population), but with a standard deviation of 12/root(50) = 1.697cm.\n\nSo the average of all these averages is 170cm - the same as the original population.  But guess you didn't want all that.\n\nCheers
710920
When working with data, skewness is the average of ((x_k-mu)/sigma)^3, where x_k are the elements of the data set, mu is the sample mean and sigma is the sample standard deviation.\n\nWhen working with random variables in probability, skewness is the mean (expected value) of ((X-mu)/sigma)^3, where X is the random variable, mu is its mean (expected value) and sigma is its standard deviation. The two definitions are analogous.\n\nThe normal distribution has skewness 0. In fact, all symmetric distributions have skewness 0. A positive skewness means that the distribution has a heavy tail to the right from the mean and it bends to the left and a negative skewness means the opposite.\n\nI'll give you a Wikipedia article although it wasn't written very well in my opinion, and I don't know if you can figure out anything from it.
584250
In statistics:\n\nmu = average = (sum of all values) / (total # of values)
920953
1) X/25\n2) X/25\n\nExplanation:\n1) If you divide a set of values by a constant, then both the mean and the standard deviation are divided by that constant.\nSince your question is about the variance, which is the SQUARE of the standard deviation, the variance is divided by the SQUARE of the constant (5, in this case).\n\n2) When you add a constant to a set of values, the mean is increased by the amount of that constant, but the standard deviation is unchanged. This is true because the group of values has all moved up by a constant amount, but their relation to each other is unchanged, and their variation from each other is unchanged. Since the standard deviation is unchanged, the variance (the square of the standard deviation) is also unchanged.
874169
There appear to be two different definitions of the standard error.\n\nThe standard error of a sample of sample size n is the sample's standard deviation divided by sqrt(n). It therefore estimates the standard deviation of the sample mean based on the population mean (Press et al. 1992, p. 465). Note that while this definition makes no reference to a normal distribution, many uses of this quantity implicitly assume such a distribution.\n\nThe standard error of an estimate may also be defined as the square root of the estimated error variance sigma^^^2 of the quantity,\ns_e=sqrt(sigma^^^2)\n\n\n\n\n    The standard error is the estimated standard deviation of a statistic. The formula depends on what statistic you are talking about. For example, the standard error of a sample mean is just the sample standard deviation divided by the square root of the sample size. For more complicated statistics, the standard error is also more complicated.\n\n    You can use the standard error in two ways. First, the statistic divided by the standard error gives you a way of testing whether the parameter that your statistic is estimating equals zero. You compare this ratio to a t-distribution. In most contexts, the ratio of the statistic divided by its standard error is called a Wald test. For many simple applications, you can also call this a t-test.\n\n    A second application of the standard error is the production of confidence intervals. You can get a crude confidence interval by taking your statistic plus or minus two standard errors. A more precise confidence interval would use percentiles from the t-distribution.\n\n    There are a lot of subtleties in the use of the standard error, especially in more complex problems. Sometimes, for example, the standard error applies not to the statistic itself, but to the logarithm of that statistic. For example, a logistic regression model will compute an odds ratio for your data, but the standard error refers not to the odds ratio, but to the log odds ratio. In this situation, you need to compute the confidence interval on the log scale and then transform the results back to the original scale of measurement.\n&#92;\n\ns
1152350
I would say variance, but I'm no statistics expert.
935234
"In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is defined as the square root of the variance.\n\nThe standard deviation is measured in the same units as the values of the population. For a population of distances in meters, the standard deviation is also measured in meters, whereas the variance is measured in square meters."\n\n\nIn essence, standard deviation is used for categorizing groups.\nFor example, the average IQ is 100, the standard deviation to the left would be 85, and deviation to the right would be 115. Two left standard deviations would be 60, two right standard deviations would be 130.\nSame applies to SAT scores, statistics, polls, etc.
187632
The relative average deviation is the average deviation divided by the average of the measurements....lol\n\nIf that doesn't help much, check out the link below.\n\nMatt
101856
Standard deviation is a measure of the variability in a sample.  A small standard deviation means that most observations are clost to the mean (average).  The standard deviation is the square root of the variance.  The variance is calculated by taking the difference between each observation and the mean, squaring it, summing for all observations, then dividing by the number of observations less one.\n\nwith m = mean and X1 ... Xn being the observations:\n\nvariance: V = [(X1-m)^2 + (X2-m)^2 ... + (Xn-m)^2] / (n-1)\nstandard deviation: sigma = sqrt(V)
935926
It means that there is a large gap in the middle of the data set with one or a small ammount of entries being grossly larger than the majority of the set:\n   the set 1,2,3,4,30 has a mean of 8 and a median of 3\n   the set 20,22,28,32,33,34,64,68,71 has a mean of 49 and \n   a median of 33
324717
what type of statistics?
149140
Don't know Levey Jennings, but in general the variance is the sum of the squared deviations from the mean divided by the number of samples (for large data sets) or the number of samples minus 1 (for smaller data sets).  The standard deviation (SD) is then the square root of the variance.\n\nSo, if "m" is the mean and each sample is x1..n, the variance is:\n\n[(m-x1)^2 + (m-x2)^2 + (m-x3)^2 ... (m-xn)^2]/n\n\nThen, take the square root of the variance to get the standard deviation.
929935
variations matter greatly in interpreting data.  Something might seem like it is returning significantly different results than the control but stat evaluation may show that the variations are minimal at best