Statistics is a science of gathering, classifying, arranging, analyzing, interpreting, and presenting the numerical data, to make inferences about the population from the sample drawn. There are basically two categories. Analytical(aka Inferential statistics) and Descriptive (aka Enumerative statistics).

Not all statistics are the same. It’s useful to discern between the various types of statistics when doing analysis. Remember;

- a statistic is a value obtained from the sample or a calculation.
- a parameter is a value found or estimated from the population.

## Analytical aka Inferential Statistics

### What are Inferential Statistics?

Inferential statistical also known as null hypothesis, use probability to determine whether a particular sample or test outcome is representative of the population from the sample was originally drawn.

Use probability to determine how confident that the conclusions are correct (use confidence interval and margin of error).

Hypothesis testing, probability distribution, regression analysis, and correlation testing comes under this category.

- Sometimes it is unrealistic to get an exhaustive population study – ex. all of America so we use a sample to infer something about the whole.
- Most of the time we infer something about the whole population.
- Developing a confidence interval is an example of using Analytical statistics.

### When do you use Inferential Statistics??

Inferential statistics is primarily used when the examination of each unit of population is not possible; therefore, it extrapolates the information received to the whole population. That way, it is useful in drawing conclusions and also decision making about the entire population based on sample data.

In other words, inferential statistics is about using sample data to make an inference or draw a conclusion of the population.

While, it is all about assessing the probability of something occurring at some point in the future or testing the population sample to generalize the result to the entire population.

### Examples of Inferential Statistics in a DMAIC Project

**Example:** Let us assume the population in Hartford County is 100,000. The state health department wishes to know how many people in the county have high blood sugar/blood glucose.

It would be unreasonable to test every individual blood sugar in the county, and it is also not practical to test 100,000 people’s blood sugar.

The best solution is to select 1000 samples from 100,000 and test the blood sugar as per health department guidelines.

For instance, let us assume 17% of people with ±1 errors have high blood sugar in the sample of 1000.

We can use this information to infer or draw a conclusion of the total population of 100,000 in Hartford county.

More precisely, we could say that 95% confidence, 17% of people live in the county has high blood sugar within a 1% margin of error.

Furthermore, to increase the confidence of the inference, increase the sample size to draw conclusion of the population. By increasing the sample size, we can better predict the high blood sugar of individuals in the population.

## Descriptive (aka Enumerative statistics)

### What are Descriptive Statistics?

A descriptive statistic is basically organizing and summarizing the data using numbers and graphs.

In the descriptive method, the data is summarized tabulated, organized, and presented in the forms of charts and graphs to summarize the data under consideration for the whole population. Furthermore, no inferences are made about the units which are not observed.

Typically used for the whole entire population, not just a sample.

- Using a graph or population parameter
- Organize or summarize information
- Measure of frequency (Count, percentage, frequency)
- The measure of central tendency (Mean, median, mode)
- Measure of dispersion or variation (Range, variation, standard deviation)

- Graphs, charts & plots

### When do you use Descriptive Statistics??

Descriptive statics is to describe the characteristics of the sample or population. It also describes the basic features of the situation, and the results are present in the forms of charts, graphs, and tables.

### Examples of Descriptive Statistics in a DMAIC Project

**Example:** Let us assume a supermarket selling 100 milk cans every day, out of which 30 are from XYZ company.

Data representation: 30% of milk cans are sold from XYZ company.

In addition, If the same supermarket conducting a study on the number of soda sold for each shift for one week and determine that average 20 sodas sold each shift. The average is an example of descriptive statistics.

The same data can be presented in a visual graphical method like histogram, pie chart or a bar graph is also comes under this category. Furthermore, the visual representation helps the organizations compare different data sets of milk cans quantity and identify the changes in the quantity over a period of time.

Further, refer here for more examples.

## Key Differences

## Inferential Vs Descriptive Statistics Video

## Helpful Articles

http://www.micquality.com/six_sigma_glossary/analytical_descriptive_statistics.htm (Descriptive vs. inferential statistics)

## ASQ Six Sigma Green Belt Kinds of Statistics Questions

**Question:** Which of the following statistics summarizes the population?

(A) categorical

(B) descriptive

(C) probabilistic

(D) control

**Answer:** (B) Descriptive statistics summarize a population. The other options are nonsensical.

## Comments (4)

3. The percentages of total quality cost are distributed as follows: prevention 12%, appraisal 28%, internal failure 40%, and external failure 20%. One would conclude:

a. More money should be invested in prevention

b. Expenditures for failures are excessive

c. The amount spent for appraisal seems about right

d. Nothing

Hi Curtler,

Would love to help. Please join my Custom tier for unlimited email support.

Best, Ted.

Ted, What is the custom tier?

Hi Terry,

Thank you for the question. The custom tier is a version of PYSSGB where candidates can get additional support. Right now you are in the Guided tier so you get access to thousands of questions across dozens of practice quizzes and exams as well as access to study materials, member forums, full question walkthroughs, and the ability to ask questions on any of the practice exams provided.

The custom tier has everything the guided tier does but enables you to ask any question you want about Six Sigma. You also get a 1:1 conversation with me to plan your strategy. This is helpful for students who feel less confident in their original instruction and need additional help preparing for their exam beyond what is offered in the guided package. In the comment above, Curtler is asking about a problem set from outside my course, hence my recommendation for the custom tier.

If anyone is interested in the custom tier, checkout is here.

Best, Ted.