| Sampling Distributions |
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| It is important to know the difference between a distribution of individuals (the parent distribution) and a distribution of averages of samples from that distribution. The sampling distribution is different from the distribution of individual observations. In general, sampling distributions are more normal and have less variability than the original distribution. Some of the cautions are on the previous page on sample means, |
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| Comparision of a distribution of individuals with a sampling distribution. |
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Figure 1. A distribution of individuals.
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Notes about the sampling distribution:
In practice individuals are included in only one sample; they are not counted twice. For instance, in sampling package weights, no package would be in two samples.
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Figure 2. A distribution of sample means.
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The histogram in figure 3 shows 500 observations (samples of size 1) taken from a normal distribution It has a bell curve shape as expected. That the shape is not quite normal is due to variability in the sample. The next sample taken will look a little different, but still reflect the normal qualities of the parent distribution. A larger number of observations would increasingly resemble the parent population--until every member of the population was included. |
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#29 The large sample in figure 3 is drawn from a normal population with a mean value of 50– we don't know what that number represents, but the average value in the population is 50.
a) What class (bin) is over-represented in this sample?
b) What cclass might be under-represented?
c) What is the approximate standard deviation of the data in the histogram?
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Figure 3. Samples from a population that is normally distributed.
The scale shows the center of each class.
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