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what information about the sample of a mean not provide

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10y ago
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11y ago

Information about the scale, spread or dispersion of the population from which the sample was drawn.

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Q: What information about a sample does a mean not provide?
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How do you find the sample size when given the standard deviation and the mean with a sample value?

You cannot from the information provided.


What happens to the sample mean as the sample size increases?

With a good sample, the sample mean gets closer to the population mean.


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What is the difference between calculating the sample mean and the population mean?

You calculate the actual sample mean, and from that number, you then estimate the probable mean (or the range) of the population from which that sample was drawn.


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What is population mean in statistics?

The population mean is the mean value of the entire population. Contrast this with sample mean, which is the mean value of a sample of the population.


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How does the addition of a constant and multiplication by a constant affect the arithmetic mean?

If you add the same constant to each element of a sample then the mean of this collection of values will be the mean of the original sample plus the constant. If you multiply each element of a sample by a constant then the mean of this collection of values will be the mean of the original sample multiplied by the constant.


Will a population mean and sample mean always be identical?

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What measure of central tendency is most stable from sample to sample?

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How is it that a random samples gives a fairly accurate representation of public opinion?

The main point here is that the Sample Mean can be used to estimate the Population Mean. What I mean by that is that on average, the Sample Mean is a good estimator of the Population Mean. There are two reasons for this, the first is that the Bias of the estimator, in this case the Sample Mean, is zero. A Bias other than zero overestimates or underestimates the Population Mean depending on its value. Bias = Expected value of estimator - mean. This can be expressed as EX(pheta) - mu (pheta) As the Sample Mean has an expected value (what value it expects to take on average) of itself then the greek letter mu which stands for the Sample Mean will provide a Bias of 0. Bias = mu - mu = 0 Secondly as the Variance of the the Sample Mean is mu/(n-1) this leads us to believe that the Variance will fall as we increase the sample size. Variance is a measure of the dispersion of values collected from the centre of the data. Where the centre of the data is a fixed value equal to the median. Put Bias and Variance together and you get the Mean Squared Error which is the error associated with using an estimator of the Population Mean. The formula for Mean Squared Error = Bias^2 + Variance With our estimator we can see that as the Bias = zero, it has no relevance to the error and as the variance falls as the sample size increases then we can conclude that the error associated with using the sample mean will fall as the sample size increases. Conclusions: The Random Sample of public opinon will on average lead to a true representation of the Population Mean and therefore the random samle you have will represnt the public opinion to a fairly high degree of accuracy. Finally, this degree of accuracy will rise incredibly quickly as the sample size rises thus leading to a very accurate representation (on average)


What does it mean for a sample to have a standard deviation of zero?

It means that there are is no variation from the mean. In other words, all values in your sample are identical.