# For Mathemathics Expert

In responses to Traci, Nathan, Krista, and Jennifer indicate what you think it is about their examples that clarify the concept “mean of the sampling distribution.” The concept is abstract, but how do their examples make it concrete and more understandable? As an alternative, you could explain how the concept of a sampling distribution pertains to inferential statistics.

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Traci post

The mean of a sampling distribution is a distribution created by every possible mean from every possible sample. When the samples used to develop each mean of the distribution are large enough, then the sampling distribution of the mean of any independent random sample will be normally distributed The larger the sample, the more likely it will have that normal bell shaped curve. This method can be useful because it can determine how accurate my chosen sample mean is from all other possible means.

Sampling Distribution Example:

Lets say I wanted to know the average birth weight of a new born baby, I think I would randomly select recorded birth weights of 50 newborns at a hospital. I would calculate the mean of birth weights for the 50 babies. I now have my first mean, let’s say I repeat the process across the nation obtaining birth weight records for newborns at 100 different hospitals, I now have 100 sets of 50 NB birth weights and 100 different means which make up the sampling distribution. To get the mean of the sampling distribution, I’d calculate the mean of all 100 means from the 100 sets of 50.

Nathan post

A sampling distribution is simply what is produced when all of the sample statistics are distributed from all necessary samples, regardless of whether or not there is a variance in size. The process of distribution, in this case, is known as the distribution of sample means, since it is used to find the mean of all possible samples (Bennett, Briggs & Triola, 2016, 270). A perfect example of can take place in a pediatrician’s office, where growth charts are utilized to monitor how a child is developing and whether or not they are sustaining a healthy BMI. A pediatrician alone may see a hundred patients, but what if that pediatrician was just a dime in a dozen and worked alongside many other pediatricians. Say, 100? Well, those pediatricians also see approximately a hundred patients too, and it just so happens that every doctor has reached their capacity. Each pediatrician also has a hundred growth charts. Therefore, the hundred growth charts each pediatrician possesses will produce an individual mean. If one were to put all of their means together, it would produce a sampling distribution, and from there, him or she can use the process of “distribution of sample means” to find the mean BMI of every single child in this obnoxiously large pediatrician’s office.

Krista post

The mean of a sampling distribution is a distribution created by every possible mean from every possible sample.

For example, if I wanted to know the average amount of children per household in North America, I could randomly select 100 households within a state to poll. I would calculate the mean of the number of children per household. Now I would repeat this process in each of the 50 states, giving 50 sets of 100-household polling, which gives 50 different means to create the sampling distribution. The mean of the sampling distribution would be the mean of all 50 means from the 50 sets of 100.

Jennifer post

A sampling distribution is a probability distribution of a statistic obtained through many samples drawn from a specific population. The sampling distribution of a given population is the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population. The number of observations in a population, the number of observations in a sample and the procedure used to draw the sample sets determine the variability of a sampling distribution. The standard deviation of a sampling distribution is called the standard error. While the mean of a sampling distribution is equal to the mean of the population, the standard error depends on the standard deviation of the population, the size of the population and the size of the sample. Knowing how spread apart the mean of each of the sample sets are from each other and from the population mean will give an indication of how close the sample mean is to the population mean. The standard error of the sampling distribution decreases as the sample size increases.

Example: The Can Equity Mortgage company, has the mean age of mortgage applicants in the city of Toronto is 37 years of age. Then assume that the standard deviation if 6 years. The find the mean and standard deviation of the sampling distribution of the sample mean for the following sample sizes: (a) 4, (b) 100, (c) 255 μx = μ = 37

(a) n = 4. Then σX−−=σ/n−−√=6/4–√=3.

(b) n = 100. Then σX−−=σ/n−−√=6/100–√=0.6

(c) n = 225. Then σX−−=σ/n−−√=6/225–√=0.4.

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