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Shape Of Sampling Distribution. 6 Figure 47 a Skewed to the left left-skewed. A sampling distribution is a probability distribution of a statistic obtained from a larger number of samples drawn from a specific population. Whereas the distribution of the population is uniform the sampling distribution of the mean has a shape approaching the shape of the familiar bell curve. As previously mentioned the overall shape of a sampling distribution is expected to be symmetric and approximately normal.
A The shape of the distribution. The shape of a distribution may be considered either descriptively using terms such as J-shaped or numerically using quantitative measures such as skewness and kurtosis. This is due to the fact or assumption that there are no outliers or other important deviations from the overall pattern. For example if you look at the amount of time X required for a clerical worker to complete a task you may find that X had a normal. A bell-shaped curve with a single peak and two tails extending symmetrically in either direction just like what we saw in previous chapters. If there appear to be two mounds we say the distribution is bimodal.
In other words the shape of the distribution of sample means should bulge in the middle and taper at the ends with a shape that is somewhat normal.
A sampling distribution refers to a probability distribution of a statistic that comes from choosing random samples of a given population. Its exactly normal because both populations are normally distributed. The shape of our sampling distribution is normal. A sampling distribution is a probability distribution of a certain statistic based on many random samples from a single population. The sampling distribution of the mean will still have a mean of μ but the standard deviation is different. In this case we say that the distribution is skewed.