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The Sampling Distribution Of The Sample Mean. When the sample size is sufficiently large the shape of the sampling distribution approximates a normal curve regardless of the shape of the parent population. Mean 8333 17 17132 8666 17466 178. 1 Sampling Distribution of Mean This can be defined as the probabilistic spread of all the means of samples chosen on a random basis of a fixed size from a particular population. Because the sampling distribution of the sample mean is normal we can of course find a mean and standard deviation for the distribution and answer probability questions about it.
Mean 8333 17 17132 8666 17466 178. Heres the type of problem you might see on the AP Statistics exam where you have to use the sampling distribution of a sample mean. μ 1 6 13 134 138 140 148 150 14 pounds The following dot plots show the distribution of the sample means corresponding to sample sizes of n 2 and of n 5. To put it more formally if you draw random samples of size n the distribution of the random variable which consists of sample means is called the sampling distribution of the sample mean. In other words regardless of whether the population distribution is normal the sampling distribution of the sample mean will always be. In the following example we illustrate the sampling distribution for the sample mean for a very small population.
Regardless of the distribution of the population as the sample size is increased the shape of the sampling distribution of the sample mean becomes increasingly bell.
The symbol mu _M is used to refer to the mean of the sampling distribution of the mean. Recall though that we computed the population mean in the lesson about population distribution and we found that μ 864. Sample Means with a Small Population. The mean of the sampling distribution of the mean is the mean of the population from which the scores were sampled. Mean 86397 and 86397 rounded to the nearest tenth is 864. The importance of the Central Limit Theorem is that it allows us to make probability statements about the sample mean specifically in relation to its value in comparison to the population mean as we will see in the examples.