yes
Chat with our AI personalities
The larger your sample size, the less variance there will be. For instance, your information is going to be much more substantial if you took 1000 samples over 10 samples.
Yes, Mean is given by, E(X) sum of samples / no. of samples. Variance is Var.(X) = E(X^2) - [E(X)]^2. It is the 1st term which makes the variation of variance independent of mean. In other words, Variance gives a measure of how far the samples are spread out.
The two distributions are symmetrical about the same point (the mean). The distribution where the sd is larger will be more flattened - with a lower peak and more spread out.
because of two things- a) both positive and negative deviations mean something about the general variability of the data to the analyst, if you added them they'd cancel out, but squaring them results in positive numbers that add up. b) a few larger deviations are much more significant than the many little ones, and squaring them gives them more weight. Sigma, the square root of the variance, is a good pointer to how far away from the mean you are likely to be if you choose a datum at random. the probability of being such a number of sigmas away is easily looked up.
That only happens when you sample a population that is normally distributed. In that case, the question and its answer are quite circular.