# Descriptive and Inferential Statistical Methods

I am in a peer/mentor group. We are meeting to discuss statistical methods. I need to discuss the goals of two statistical methods.

The statistical methods are to be selected by you. What are some statistical methods? What does each method attempt to accomplish? I only need to address two.

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Please refer to attached file response, also presented below. I also included a highly relevant article, one that you may find helpful. I hope this helps and take care.

RESPONSE:

Your questions are these: "What are some statistical methods? What does each method attempt to accomplish? I only need to address two."

1. Descriptive Statistical Methods

Descriptive Statistics utilizes numerical and graphical methods to look for patterns, to summarize, and to present the information in a set of data. Some examples of graphic description of data sets, as well as what each method accomplishes, are as follows:

a. Stem and Leaf Plot

A stem and leaf plot is a way of summarizing a set of data measured on an interval scale. It is often used in exploratory data analysis to illustrate the major features of the distribution of the data in a convenient and easily drawn form.

A stem and leaf plot is similar to a histogram but is usually a more informative display for relatively small data sets (<100 data points). It provides a table as well as a picture of the data and from it we can readily write down the data in order of magnitude, which is useful for many statistical procedures.

We can compare more than one data set by the use of multiple stem and leaf plots. By using a back-to-back stem and leaf plot, we are able to compare the same characteristic in two different groups, for example, pulse rate after exercise of smokers and non-smokers.

b. Box and Whisker Plot (or Box plot)

A box and whisker plot is a way of summarizing a set of data measured on an interval scale. It is often used in exploratory data analysis. It is a type of graph, which is used to show the shape of the distribution, its central value, and variability. The picture produced consists of the most extreme values in the data set (maximum and minimum values), the lower and upper quartiles, and the median.

A box plot (as it is often called) is especially helpful for indicating whether a distribution is skewed and whether there are any unusual observations (outliers) in the data set.

Box and whisker plots are also very useful when large numbers of observations are involved and when two or more data sets are being compared.

Inter-Quartile Range (IQR)

The inter-quartile range is a measure of the spread of or dispersion within a data set.

It is calculated by taking the difference between the upper and the lower quartiles. For example:

Data 2 3 4 5 6 6 6 7 7 8 9

Upper quartile 7

Lower quartile 4

IQR 7 - 4 = 3

The IQR is the width of an interval which contains the middle 50% of the sample, so it is smaller than the range and its value is less affected by outliers.

c. 5-Number Summary

A 5-number summary is especially useful when we have so many data that it is sufficient to present a summary of the data rather than the whole data set. It consists of 5 values: the most extreme values in the data set (maximum and minimum values), the lower and upper quartiles, and the median.

A 5-number summary can be represented in a diagram known as a box and whisker plot. In cases where we have more than one data set to analyze, a 5-number summary is constructed for each, with corresponding multiple box and whisker plots.

d. Histogram

A histogram is a way of summarizing ...

#### Solution Summary

This solution explains descriptive and inferential statistical methods in terms of definition and goals. Specifically, examples of descriptive statistics are explained (e.g. stem and plot, histogram, etc.) as well as the step-by step process of inferential statistics. Nominal, ordinal, interval, and categorical data are described and summarized using descriptive statistical method(s) using illustrate examples illustrating a step-by-step process (e.g., frequency table, whisker Plot or boxplot). Supplemented with one exceptionally informative article on inferential statistical methods.