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I will restate your question as "Why are the mean and standard deviation of a sample so frequently calculated?". The standard deviation is a measure of the dispersion of the data. It certainly is not the only measure, as the range of a dataset is also a measure of dispersion and is more easily calculated. Similarly, some prefer a plot of the quartiles of the data, again to show data dispersal.t Standard deviation and the mean are needed when we want to infer certain information about the population such as confidence limits from a sample. These statistics are also used in establishing the size of the sample we need to take to improve our estimates of the population. Finally, these statistics enable us to test hypothesis with a certain degree of certainty based on our data. All this stems from the concept that there is a theoretical sampling distribution for the statistics we calculate, such as a proportion, mean or standard deviation. In general, the mean or proportion has either a normal or t distribution. Finally, the measures of dispersion will only be valid, be it range, quantiles or standard deviation, require observations which are independent of each other. This is the basis of random sampling.
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When do you use the relative standard deviation instead of standard deviation?
Use %RSD when comparing the deviation for popolations with different means. Use SD to compare data with the same mean.
Variance and standard deviation are one and the same thing?
No. But they are related. If a sample of size n is taken, a standard deviation can be calculated. This is usually denoted as "s" however some textbooks will use the symbol, sigma. The standard deviation of a sample is usually used to estimate the standard deviation of the population. In this case, we use n-1 in the denomimator of the equation. The variance of the sample is the square of the sample's standard deviation. In many textbooks it is denoted as s2. In denoting the standard deviation and variance of populations, the symbols sigma and sigma2 should be used. One last note. We use standard deviations in describing uncertainty as it's easier to understand. If our measurements are in days, then the standard deviation will also be in days. The variance will be in units of days2.
Are standard deviation and mean use for ratio data?
Yes.
When to use z or t-distribution?
If the sample size is large (>30) or the population standard deviation is known, we use the z-distribution.If the sample sie is small and the population standard deviation is unknown, we use the t-distribution
When we know the population mean but not the population standard deviation which statistic do we use to compare a sample to the population?
The sample standard error.
