The mean, by itself, does not provide sufficient information to make any assessment of the sample variance.
"The advantage is that the mean takes every value into account. A disadvantage is that it can be affected by extreme values. " The mean or more properly the "arithmetic mean" of a sample will eventually approximate the mean of the distribution of the population as the sample size increases. If the population distribution is skewed (not symmetrical), the mode and median will not provide an estimate of the mean, even as the sample size becomes large.
The sample mean may differ from the population mean, especially for small samples.
What is the sample mean?
The same basic formula is used to calculate the sample or population mean. The sample mean is x bar and the population mean is mu. Add all the values in the sample or population and divide by the number of data values.
You cannot from the information provided.
With a good sample, the sample mean gets closer to the population mean.
Please provide more information, what do you 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.
IF you mean literally a goldfish, no. Just no. Otherwise provide information on what you mean by a "goldfish".
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.
yes
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.
The sample mean will seldom be the same as the population mean due to sampling error. See the related link.
Statistically speaking, the mean is the most stable from sample to sample. Whereas, the mode is the least stable statistically speaking from sample to sample.
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)
It means that there are is no variation from the mean. In other words, all values in your sample are identical.