Question

. Describe the major differences between sampling distributions that contain sample means and frequency distributions containing individual scores.

Answer 1

The Sampling Distribution of the Sample Mean

If repeated random samples of a given size n are taken from a population of values for a quantitative variable, where the population mean is μ (mu) and the population standard deviation is σ (sigma) then the mean of all sample means (x-bars) is population mean μ (mu).

As for the spread of all sample means, theory dictates the behavior much more precisely than saying that there is less spread for larger samples. In fact, the standard deviation of all sample means is directly related to the sample size, n as indicated below.

Since the square root of sample size n appears in the denominator, the standard deviation does decrease as sample size increases.

Frequency Distribution containing individual score

Goal: simplify the organization and presentation of data

Definition: lists or displays graphically the number of individuals located in each category on the scale of measurement

-  takes a disorganized set of scores and places them in order from highest to lowest, grouping together all individuals who have the same score

-  see the set of scores “at a glance”

-  frequency distribution can be structured either as a table or graph.