Question

How does the variability of a distribution of means relate to the variability of a distribution of individual observations? How do differences in variability affect the shape of a distribution? Explain in your own words.

Answer 1

ANSWER::

Sampling distribution of mean follows the same distri ition as individual observations do. Suppose X1, X2,..., Xn are independent observations from a normal population with mean mu and variance sigma square.

Then, the distribution of sample mean would also follow the normal distribution with mean mu and variance sigma square/n. The variability of distribution of mean is directly proportional to the variability of individual observations in this example.

A probability curve of distribution with large variability would be flat compared with a probability curve of distribution with relatively less variability.

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