Question

Write a paragraph about sampling distributions that explain In detail what the key concepts mean. You can use examples to help in your explanation.

Answer 1

Solution :-

The sampling distribution of a statistic is the distribution of the statistic for all possible samples from the same population of a given size.

The sampling distribution depends on: the underlying distribution of the population, the statistic being considered, the sampling procedure employed, and the sample size used.

For example, consider a normal population with mean μ and variance σ. Assume we repeatedly take samples of a given size from this population and calculate the arithmetic mean for each sample. This statistic is then called the sample mean. Each sample has its own average value, and the distribution of these averages is called the “sampling distribution of the sample mean. ” This distribution is normal since the underlying population is normal, although sampling distributions may also often be close to normal even when the population distribution is not.

An alternative to the sample mean is the sample median. When calculated from the same population, it has a different sampling distribution to that of the mean and is generally not normal (but it may be close for large sample sizes).

More Properties of Sampling Distributions

1. The overall shape of the distribution is symmetric and approximately normal.
2. There are no outliers or other important deviations from the overall pattern.
3. The center of the distribution is very close to the true population mean.

Finally, the variability of a statistic is described by the spread of its sampling distribution. This spread is determined by the sampling design and the size of the sample. Larger samples give smaller spread. As long as the population is much larger than the sample (at least 10 times as large), the spread of the sampling distribution is approximately the same for any population size

A sampling distribution is a graph of a statistic for your sample data. While, technically, we could choose any statistic to paint a picture, some common ones we’ll come across are:

• Mean
• Mean absolute value of the deviation from the mean
• Range
• Standard deviation of the sample
• Unbiased estimate of variance
• Variance of the sample