# Using statistical thinking and summarizing data

Debates on its emergence as a strategic initiative have created critics who consider it old wine in a new bottle and loyal followers willing to swear by it. The latter of these are practitioners who view Six Sigma as an effective way to implement statistical thinking, a philosophy of learning and action based on the following fundamental principles: All work occurs in a system of interconnected processes Variation exists in all processes Understanding and reducing variation are the keys to success Statistical thinking provides practitioners with the means to view processes holistically. A specific quantile or percentile is a value in the data set that holds a specific percentage of the values at or below it. The median is the 50th percentile, the third quartile is the 75th percentile and the maximum is the th percentile i. A box-whisker plot is a graphical display of these percentiles. The horizontal lines represent from the top the maximum, the third quartile, the median also indicated by the dotthe first quartile and the minimum. A box-whisker plot is meant to convey the distribution of a variable at a quick glance. Recall that in the full sample we determined that there were outliers both at the low and the high end See Table In Figure 12 the outliers are displayed as horizontal lines at the top and bottom of the distribution.

At the low end of the distribution, there are 5 values that are considered outliers i. At the high end of the distribution, there are 12 values that are considered outliers i. The "whiskers" of the plot boldfaced horizontal brackets are the limits we determined for detecting outliers Figure 13 below shows side-by-side box-whisker plots of the distributions of weights, in pounds, for men and women in the Framingham Offspring Study.

The figure clearly shows a shift in the distributions with men having much higher weights. In fact, the 25th percentile of the weights in men is approximately pounds and equal to the 75th percentile in women.

There are many outliers at the high end of the distribution among both men and women. There are two outlying low values among men.

## Calendar | Statistical Thinking and Data Analysis | Sloan School of Management | MIT OpenCourseWare

There are again many outliers in the distributions in both men and women. However, when taking height into account by comparing body mass index instead of comparing weights alonewe see that the most extreme outliers are among the women. Some statistical computing packages use the following to determine outliers: Summary The first important aspect of any statistical analysis is an appropriate summary of the key analytic variables.

This involves first identifying the type of variable being analyzed. This step is extremely important as the appropriate numerical and graphical summaries depend on the type of variable being analyzed. Variables are dichotomous, ordinal, categorical or continuous.

The best numerical summaries for dichotomous, ordinal and categorical variables involve relative frequencies. The best numerical summaries for continuous variables include the mean and standard deviation or the median and interquartile range, depending on whether or not there are outliers in the distribution.

The mean and standard deviation or the median and interquartile range summarize central tendency also called location and dispersion, respectively.

## Key components to a statistical investigation are:

The best graphical summary for dichotomous and categorical variables is a bar chart and the best graphical summary for an ordinal variable is a histogram. Both bar charts and histograms can be designed to display frequencies or relative frequencies, with the latter being the more popular display.

Box-whisker plots provide a very useful and informative summary for continuous variables. Box-whisker plots are also useful for comparing the distributions of a continuous variable among mutually exclusive i.

The following table summarizes key statistics and graphical displays organized by variable type.This material is about summarizing and analyzing data by using statistical methods. It gives you an overall picture on using statistical methods in decision making.

Usually you need to prepare data before doing any analyses.

## Summarizing Data

In chapter 2 DATA SET you find valuable Excel Critical thinking. If your data contains more than one mode, then summarizing them with a simple measure of central tendency such as the mean or median will obscure this fact. Table 1 is a quick guide to help you decide which measure of central tendency to use with your data.

Statistics – A guide. These pages are aimed at helping you learn about statistics. Why you need them, what they can do for you, which routines are suitable for your purposes and how to carry out a range of statistical analyses. On this page: Summarizing data.

Statistics, Data, and Statistical Thinking The Science of Statistics Types of Statistical Applications Fundamental Elements of Statistics Types of Data Collecting Data The Role of Statistics in Critical Thinking Chapter - Measures of Variability Chapter - Describe data using Mean & SD Chapter - Measures of.

Statistics, Data, and Statistical Thinking. Statistical thinking. Involves applying rational thought to assess data and the inferences made from them critically. ashio-midori.com be found using formula, for grouped data Or where score is repeated [like formula for median] Percentile Rank.

Statistical thinking involves the careful design of a study to collect meaningful data to answer a focused research question, detailed analysis of patterns in the data, and drawing conclusions that go beyond the observed data.

DataAnalytics: Statistics - A guide - Summarizing Data