SQL Server Reference Guide

Mar 28, 2003

␡

⎙ Print

< Back Page 151 of 365 Next >

Design Elements Part 8: Summarization Statistical Algorithms

In last week's tutorial, we learned the importance of applying statistical methods properly. We covered the basics of statistics and where they are used.

To properly use statistical data, we need to collect, store and analyze it correctly. The statistical method we're using is to ask the questions, collect the data, and analyze the results. While this might sound obvious, each steps has a specific discipline to follow.

The primary uses of statistical analysis are summarizing data, grouping (or representing) data, comparing data sets, showing the differences between data sets, and finding relationships between data sets. We began the topic of summarizing data, in the context of SQL databases (and SWL Server in particular), which we'll finish today.

The first two functions we used for summarizing data were the SUM() and COUNT() functions. These are both quite basic, and the only real twist related to either of them is that we can use limiting queries to get only the results we're looking for.

SQL Server provides a built-in function for this formula: AVG(). The proper statistical name for this type of average is the mean. The problem is that a mean isn't really perfect. What we're trying to show is a representation of a data set. The simple formula above tends to do that – sometimes. For instance, if the average of a set of coins is five cents, we don't really know if we have a quarter and five pennies or six nickels.

For this reason, the mean is best used in conjunction with other tools that summarize the data. This is an important concept to learn about applying statistical methods. When you see a single statistic provided from an unqualified data sample, don't implicitly trust the conclusions.

Another type of summarization method to use is to show the middle number in a set, called the median. That gives us more confidence in the characterization of the data. It's a simple enough formula: we just take the data set, order it from lowest to highest, and then divide the set in half. The problem is, although it's a simple formula, there's no direct formula for it in T-SQL. We have to do a little work to get there, but it's not that hard.

To find the median, we just follow the formula. You'll need to make use of one new construct – the temporary table. A temporary table is a table constructed in memory, and is available only to the connection that creates it. When the connection is broken, the table is destroyed.

NOTE

There's another type of temporary table which is available to more than one connection, called a global temporary table.

Youe create a temporary table the same way as a normal table, except that you preface the name with a # sign for the local type, and ## for the global ones.

So we'll create a temporary table, insert the data in the table using a subquery, sorted in the right order. We've seen all these constructs before, but the twist is that we'll use an identity data type to provide a numerical reference for the middle value. Then we'll create variables to hold the numbers and calculations, and then use them to locate the center value, or at least the one closest to it.

Here's the code:

USE pubs
GO

-- Create a temporary table to hold the values
-- and an identity field to give us a row-holder.
-- Note - Median would need to have another type 
-- if the value isn't numeric
CREATE TABLE #Median(Median int, ID int identity) 

-- Fill the temporary table with an ordered list from 
-- the source base table
INSERT INTO #Median (Median) 
 SELECT qty 
 FROM sales
 ORDER BY qty ASC

-- Set up variables to hold the calculations
DECLARE @Count AS INT, @Median AS INT 

-- Get the number of rows from the ordered temporary table
SET @Count = (SELECT COUNT(*)FROM #Median) 

-- Find the middle (roughly)
SET @Median = (@Count/2) 

-- Use that value to find the proper value 
-- from the ordered list
SELECT Median from #Median where ID = @Median 

-- Clean up
DROP TABLE #Median

GO

We now have four formulas to work with to help summarize the data, SUM(), COUNT(), AVG(), and our new median algorithm. But that's not all. To truly understand these numbers, we have a few more formulas to work out.

The first is the Mode. A mode is the number found most often in the data set. The mode, along with the average and median, can help us have confidence in the numbers closest to the average. The more numbers that are around the average, the more confidence we can have in it.

Once again, T-SQL does not provide a formula for this statistical function. We can, however, use a simple GROUP BY aggregate with the TOP function to get at it:

SELECT TOP 1 COUNT(*) as 'Number of repeats'
, qty as 'Number' 
FROM sales
GROUP BY qty
ORDER BY COUNT(*) DESC

The final three functions have the formulas built-in.

The next two formulas show our range, or the spread of the values. The ranges of the numbers show us the high and low values of the data set.

Here are both of them in code:

SELECT MAX(qty) as 'Maximum value'
, MIN(qty) as 'Minimum value'
FROM sales

Finally, we need to know how far the numbers are spread around the average. If the spread is quite large, we have less confidence in the average. The function T-SQL provides for this measurement is STDEV(), and it takes a column as a parameter. Here's how that looks:

SELECT STDEV(qty) as 'Standard Deviation'
FROM sales

With a standard deviation, about 65% of the values in the set are within one standard deviations of the mean. For example, if the average is 12, and the standard deviation is 1, then 65% of the values are between 11 and 13. More than 90% of the sets' values are within two standard deviations, so most of the data in this example is between 10 and 14! That gives us a great reassurance that the mean represents the data.

So, having the average is fine – provided we also know the standard deviation.

Finally, we can look at the variance of the distribution of the data. The variance also shows how tightly the data is clustered around the mean; it's just the square of the standard deviation. Here's that function:

 SELECT VAR(qty) as 'Variance'
 FROM sales

All these functions and algorithms show us the summarization functions. Next week, we'll recap with a combination of all these numbers, and a handy table that shows when to use each.

Online Resources

If you're really interested in the formulas behind these algorithms, this statistics glossary can't be beat.

< Back Page 151 of 365 Next >

🔖 Save To Your Account

InformIT Promotional Mailings & Special Offers

I would like to receive exclusive offers and hear about products from InformIT and its family of brands. I can unsubscribe at any time.

Privacy Notice

Overview

Pearson Education, Inc., 221 River Street, Hoboken, New Jersey 07030, (Pearson) presents this site to provide information about products and services that can be purchased through this site.

This privacy notice provides an overview of our commitment to privacy and describes how we collect, protect, use and share personal information collected through this site. Please note that other Pearson websites and online products and services have their own separate privacy policies.

Collection and Use of Information

To conduct business and deliver products and services, Pearson collects and uses personal information in several ways in connection with this site, including:

Questions and Inquiries

For inquiries and questions, we collect the inquiry or question, together with name, contact details (email address, phone number and mailing address) and any other additional information voluntarily submitted to us through a Contact Us form or an email. We use this information to address the inquiry and respond to the question.

Online Store

For orders and purchases placed through our online store on this site, we collect order details, name, institution name and address (if applicable), email address, phone number, shipping and billing addresses, credit/debit card information, shipping options and any instructions. We use this information to complete transactions, fulfill orders, communicate with individuals placing orders or visiting the online store, and for related purposes.

Surveys

Pearson may offer opportunities to provide feedback or participate in surveys, including surveys evaluating Pearson products, services or sites. Participation is voluntary. Pearson collects information requested in the survey questions and uses the information to evaluate, support, maintain and improve products, services or sites, develop new products and services, conduct educational research and for other purposes specified in the survey.

Contests and Drawings

Occasionally, we may sponsor a contest or drawing. Participation is optional. Pearson collects name, contact information and other information specified on the entry form for the contest or drawing to conduct the contest or drawing. Pearson may collect additional personal information from the winners of a contest or drawing in order to award the prize and for tax reporting purposes, as required by law.

Newsletters

If you have elected to receive email newsletters or promotional mailings and special offers but want to unsubscribe, simply email information@informit.com.

Service Announcements

On rare occasions it is necessary to send out a strictly service related announcement. For instance, if our service is temporarily suspended for maintenance we might send users an email. Generally, users may not opt-out of these communications, though they can deactivate their account information. However, these communications are not promotional in nature.

Customer Service

We communicate with users on a regular basis to provide requested services and in regard to issues relating to their account we reply via email or phone in accordance with the users' wishes when a user submits their information through our Contact Us form.

Other Collection and Use of Information

Application and System Logs

Pearson automatically collects log data to help ensure the delivery, availability and security of this site. Log data may include technical information about how a user or visitor connected to this site, such as browser type, type of computer/device, operating system, internet service provider and IP address. We use this information for support purposes and to monitor the health of the site, identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents and appropriately scale computing resources.

Web Analytics

Pearson may use third party web trend analytical services, including Google Analytics, to collect visitor information, such as IP addresses, browser types, referring pages, pages visited and time spent on a particular site. While these analytical services collect and report information on an anonymous basis, they may use cookies to gather web trend information. The information gathered may enable Pearson (but not the third party web trend services) to link information with application and system log data. Pearson uses this information for system administration and to identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents, appropriately scale computing resources and otherwise support and deliver this site and its services.

Cookies and Related Technologies

This site uses cookies and similar technologies to personalize content, measure traffic patterns, control security, track use and access of information on this site, and provide interest-based messages and advertising. Users can manage and block the use of cookies through their browser. Disabling or blocking certain cookies may limit the functionality of this site.

Do Not Track

This site currently does not respond to Do Not Track signals.

Security

Pearson uses appropriate physical, administrative and technical security measures to protect personal information from unauthorized access, use and disclosure.

Children

This site is not directed to children under the age of 13.

Marketing

Pearson may send or direct marketing communications to users, provided that

Pearson will not use personal information collected or processed as a K-12 school service provider for the purpose of directed or targeted advertising.
Such marketing is consistent with applicable law and Pearson's legal obligations.
Pearson will not knowingly direct or send marketing communications to an individual who has expressed a preference not to receive marketing.
Where required by applicable law, express or implied consent to marketing exists and has not been withdrawn.

Pearson may provide personal information to a third party service provider on a restricted basis to provide marketing solely on behalf of Pearson or an affiliate or customer for whom Pearson is a service provider. Marketing preferences may be changed at any time.

Correcting/Updating Personal Information

If a user's personally identifiable information changes (such as your postal address or email address), we provide a way to correct or update that user's personal data provided to us. This can be done on the Account page. If a user no longer desires our service and desires to delete his or her account, please contact us at customer-service@informit.com and we will process the deletion of a user's account.

Choice/Opt-out

Users can always make an informed choice as to whether they should proceed with certain services offered by InformIT. If you choose to remove yourself from our mailing list(s) simply visit the following page and uncheck any communication you no longer want to receive: www.informit.com/u.aspx.

Sale of Personal Information

Pearson does not rent or sell personal information in exchange for any payment of money.

While Pearson does not sell personal information, as defined in Nevada law, Nevada residents may email a request for no sale of their personal information to NevadaDesignatedRequest@pearson.com.

Supplemental Privacy Statement for California Residents

California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

Sharing and Disclosure

Pearson may disclose personal information, as follows:

As required by law.
With the consent of the individual (or their parent, if the individual is a minor)
In response to a subpoena, court order or legal process, to the extent permitted or required by law
To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
To investigate or address actual or suspected fraud or other illegal activities
To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.

Links

This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.

Requests and Contact

Please contact us about this Privacy Notice or if you have any requests or questions relating to the privacy of your personal information.

Changes to this Privacy Notice

We may revise this Privacy Notice through an updated posting. We will identify the effective date of the revision in the posting. Often, updates are made to provide greater clarity or to comply with changes in regulatory requirements. If the updates involve material changes to the collection, protection, use or disclosure of Personal Information, Pearson will provide notice of the change through a conspicuous notice on this site or other appropriate way. Continued use of the site after the effective date of a posted revision evidences acceptance. Please contact us if you have questions or concerns about the Privacy Notice or any objection to any revisions.

Last Update: November 17, 2020

Email Address