Plasma Antennas announced its mmWave Plasma Silicon Antenna (PSiAN) for use in smartphones and other consumer electronics, delivering high throughput with low-latency and utilizing directional beams that generate less interference and maximize energy efficiency. https://goo.gl/o7jd9H #5G #IoT #5GWorld
Gems in SAP Cloud Platform Security – “Don’t let your Heartbleed, Cloud Platform!”
SAP Cloud Platform is an essential ingredient of SAP’s digital strategy. It is the platform for our customers’ and partners’ transformation journey towards digital business models and thus is of utmost importance for SAP.
And so is security in SAP Cloud Platform!
New Year’s Eve 2011.
11:59 PM.
Robin Seggelmann, a Germany-based developer, didn’t know at that point that he
was about to become famous a few years later in 2014. At least in some sense…
It was the moment when Seggelmann submitted coding in OpenSSL which,
by mistake, introduced a vulnerability that has later been described as a
“catastrophic” flaw in “Transport Layer Security” (TLS).
OpenSSL is an Open Source project.
“But, hey, isn’t Open Source software more secure per se? The more people review the code, the more secure it will be!”
“It’s unfortunate that it’s used by millions of people, but only very few actually contribute to it,” Seggelmann said in an interview.
Small funding, missing resources. And a bug which went unnoticed for more than two years. A bug which led to “Heartbleed”, impacting business users and private users on the Internet around the globe…
That’s why we at SAP go far beyond merely consuming Open Source Software.
Within our SAP Cloud Platform, we know the benefits of using Open Source very well as we rely significantly on Cloud Foundry. This strategic approach allows developers out there to create new and innovative Cloud Foundry-based applications that run on SAP Cloud Platform. With SAP’s engagement in the Cloud Foundry open source project, the ecosystem, and community around it, it was clear that we also actively contribute to the security of Cloud Foundry.
We do this in different ways:
* Reuse knowledge: Increase the level of security of the components in use
* Share Knowledge: Contribute back into the Open Source community
As the “Heartbleed” example showed: Open Source components can contain vulnerabilities just like any other piece of software could. Reuse knowledge aims on minimizing that risk. At SAP, we follow a professional tool-supported approach for this. It comprises а vulnerability assessment tool and notification service which provides the list of publicly known security vulnerabilities. It is complemented by a program analysis tool that helps developers identify, assess, and mitigate vulnerabilities in the open-source dependencies of Java applications.
With all the expertise we have in-house, contributing back into the Open Source community is another key pillar of increasing the overall security level of Cloud Foundry. Share knowledge bundles a variety of activities in that sense, based on the experience that the team developing on Cloud Foundry gathered. They are the ones who enhanced the central Cloud Foundry identity management service UAA – User Account and Authentication – for enterprise readiness. Their contribution consists of
* contributing code changes for strategic parts, e.g. additional authentication flows, performance improvements, and fixes to security vulnerabilities
* reporting identified vulnerabilities & threats and
* publishing threat models together with the community.
There is one more aspect of Open Source usage with Cloud Foundry for SAP, though. It allows us to Differentiate, as we develop enterprise-grade security features within UAA which remain SAP’s assets. Moreover, we work on implementing a next level of security with self-defending applications. During run-time, the system is able to identify pieces of information which are fed as input and can be compared to accepted structures – dynamic information flow tracking. For this purpose we implement parsers that refuse code execution once they encounter unexpected code tokens.
In a nutshell, we see the combination of enterprise software and Open Source as a brilliant opportunity. Or, as Bernd Leukert, member of the SAP Executive Board responsible for Products & Innovation, put it: “I … see big potential in combining the good of both worlds as well as overcoming the challenges both worlds are facing. Open Source does not equal free software; it is rather focused on community building and participation in communities by contributions.”
“Gems in Cloud Platform Security” is a new series of blogs. It takes you on a tour to discover how security is seamlessly woven into the success of SAP Cloud Platform.
More information:
Bernd Leukert’s blog “Open Source – Not a one-way street”
Press release on SAP and Cloud Foundry (2014)
Read other blogs in the “Gems in SAP Cloud Platform Security” series:
Gems in SAP Cloud Platform Security – “FIPS – Encryption is Key”
Gems in SAP Cloud Platform Security – “How to seamlessly integrate with Microsoft and Google”
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SAP Introduces Intelligent HR Solution to Help Businesses Eliminate Bias
LAS VEGAS — SAP SE (NYSE: SAP) today announced the planned release of its new job analyzer functionality embedded within the SAP SuccessFactors Recruiting Management solution to help organizations craft effective, competitive job descriptions and eliminate unconscious bias in recruiting.
—
*
Job analyzer uses machine learning to address gender bias
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The functionality supports corporate talent objectives by using machine learning algorithms to predict and flag language that reflects gender bias during the recruitment process. With this new functionality, organizations are empowered to expand their talent pools and target the best candidates for every role. The announcement was made at the 2017 HR Technology Conference & Expo, taking place October 10-13 at The Venetian in Las Vegas.
Available in beta in the fourth quarter of 2017, the job analyzer functionality enables businesses to further integrate diversity and inclusion considerations into key talent management decisions. The new functionality utilizes SAP Leonardo Machine Learning capabilities to help managers and recruiters identify and eliminate gender-biased language from job descriptions. This results in an expanded, richer applicant pool, which helps enable business leaders to reach the most qualified candidates for every position. With the power of external data, hiring managers can analyze market competitiveness and salary ranges and scrub bias language from jobs descriptions for a broader and deeper solution for the global shortage of talent.
“Many businesses continue to have unintended blind spots when it comes to their hiring practices, and this is stopping them from finding the best talent,” said Greg Tomb, president, SAP SuccessFactors*. “We are introducing digital innovation with machine learning to help HR teams uncover new insights across the full range of HR processes, in this case to support unbiased decision making in the hiring process. With the job analyzer, leaders are better positioned to attract and engage the best available people, which equates to a stronger business impact.”
SAP is also expanding its Business Beyond Bias focus to help companies optimize existing features throughout the SAP SuccessFactors HCM Suite to eliminate inherent biases around age, ethnicity, and differently-abled and LGBT communities.
“The global workforce is increasingly diverse, with more employees of different backgrounds and perspectives joining the labor market each day,” said Lisa Rowan, research vice president, HR, talent and learning strategies, IDC. “At the same time, companies worldwide are facing widening talent shortages that they are struggling to address. With these tools available throughout the SAP SuccessFactors HCM Suite, customers are better placed to remove the blind spots that are hindering them from attracting, selecting, engaging and advancing the best talent.”
These new capabilities are the latest to be delivered across the SAP SuccessFactors solutions to help organizations eliminate unconscious bias across the entire employee lifecycle. Prior deliveries include:
* Calibration: Enhancements within the SAP SuccessFactors Performance & Goals solution include photoless calibration and calibration analysis by diversity rules, such as in-app nine-box descriptors, which help ensure consistent, equitable standards in evaluating performance, potential and promotion eligibility.
* Mentoring: Functionality within the SAP SuccessFactors Succession & Development solution enables HR to match mentors and mentees based on skills and competencies to help ensure mentoring is equitable and inclusive.
* Workforce analytics: Data analysis capabilities within the SAP SuccessFactors Workforce Analytics solution enables businesses to highlight areas where diversity and inclusion targets are not being met, to visualize and forecast diversity trends in their organization and to give executives greater insight into their diversity and inclusion efforts.
The Business Beyond Bias product initiative from SAP has been recognized as Awesome New Technologies for HR by HR Tech Conference. Amy Wilson, head of product at SAP SuccessFactors, will showcase the new capabilities during the award session, taking place from 3:30 p.m. to 4:30 p.m., Wednesday, Oct. 11. Prior to that, Wilson and Debra Plousha Moore, system chief of staff and executive vice president at Carolinas HealthCare System, will discuss “How Carolinas HealthCare System Moves Its Business Beyond Bias” from 11:00 a.m. to noon, Wednesday, Oct. 11. Wilson spoke about “The ROI of Women Investing in Women” during HR Tech’s “Women in HR Technology” summit from 10:30 a.m. to 11:15 a.m., Tuesday, Oct. 10.
To learn more about how SAP SuccessFactors HCM Suite can help create a more diverse and inclusive workforce and move business beyond bias, access a new e-book here.
For more information, visit the SAP SuccessFactors website and the SAP News Center. Follow SAP on Twitter at @SuccessFactors and @sapnews.
About SAP
As market leader in enterprise application software, SAP (NYSE: SAP) helps companies of all sizes and industries run better. From back office to boardroom, warehouse to storefront, desktop to mobile device – SAP empowers people and organizations to work together more efficiently and use business insight more effectively to stay ahead of the competition. SAP applications and services enable more than 355,000 business and public sector customers to operate profitably, adapt continuously, and grow sustainably. For more information, visit www.sap.com.
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For customers interested in learning more about SAP products:
Global Customer Center: +49 180 534-34-24
United States Only: 1 (800) 872-1SAP (1-800-872-1727)
For more information, press only:
Geraldine Lim, SAP, +1 (415) 418-0945, geraldine.lim@sap.com, PT
SAP News Center press room; press@sap.com
Tim Scarfe, LEWIS Communications, +1 (510) 399-9032, tim.scarfe@teamlewis.com, PT
*SAP SuccessFactors is a brand name launched in January 2016 and is used here to mean the offerings, employees, and business of acquired company SuccessFactors, which continues to be our legal entity until integration with SAP is complete.
Any statements contained in this document that are not historical facts are forward-looking statements as defined in the U.S. Private Securities Litigation Reform Act of 1995. Words such as “anticipate,” “believe,” “estimate,” “expect,” “forecast,” “intend,” “may,” “plan,” “project,” “predict,” “should” and “will” and similar expressions as they relate to SAP are intended to identify such forward-looking statements. SAP undertakes no obligation to publicly update or revise any forward-looking statements. All forward-looking statements are subject to various risks and uncertainties that could cause actual results to differ materially from expectations. The factors that could affect SAP’s future financial results are discussed more fully in SAP’s filings with the U.S. Securities and Exchange Commission (“SEC”), including SAP’s most recent Annual Report on Form 20-F filed with the SEC. Readers are cautioned not to place undue reliance on these forward-looking statements, which speak only as of their dates.
© 2017 SAP SE. All rights reserved.
SAP and other SAP products and services mentioned herein as well as their respective logos are trademarks or registered trademarks of SAP SE in Germany and other countries. Please see http://www.sap.com/corporate-en/legal/copyright/index.epx#trademark for additional trademark information and notices. http://bit.ly/2yqvsRt #SAP #SAPCloud #AI
Statistical Inferences from Performance Data of Application
Abstract
Performance tests are crucial for any web or customer application. They reveal how a system behaves and responds during various situations. The system may run very fine with 1000 concurrent users but how would it behave when 100,000 users are logged on? In terms of performance, it means to achieve high speed, scalability, and stability of the system. There are different tools which gives different performance numbers to measure these Key performance indicators like Response time, CPU time, DB time etc. with respect to single user or multiple user tests.
However, just merely getting these performance numbers is not enough as it only conveys whether the current performance value indicates a good performance or bad performance. There is need of additional statistical inferences to be drawn out of these indicative numbers. The paper presented below talks about how we can draw statistical inferences, build relationships between different Key performance indicators of any web application, predict futuristic probabilities charts and conduct hypothesis tests and perform regression analysis
Introduction
In today’s business world, to enhance productivity of any website system, whether it be a personal project, a business venture or otherwise, it’s critical a web application is tested for its responsiveness in terms of its stability, i.e. how well it can handle specified or expected workload. Through software performance testing, efficiency of any vital application can be measured, which would help to understand the good or bad behavior of the application [4].
Non-performant (i.e., badly performing) applications generally don’t deliver their intended benefit to an organization; they add to net cost of time and money and a loss of reputation from the application users, and therefore considered as non-reliable or loss to the organization [2]. If a software application is not delivering its intended service in a performant and highly reliable manner, this leads to detrimental effect on everyone involved with the products, right from the designers, architects, coders, testers and end users [3].
With so much essence for Performance testing, yet it continues to be pretermitted in contrast to functional tests, which are well understood and have a high maturity level in most business organizations. It is truly inconceivable that companies continue to overlook the significance of performance testing while frequently creating and deploying applications with
negligible or no understanding of their performance, and eventually beleaguered with performance and scalability issues after the release. However, over course of several years this mindset has changed and organizations started caring to check for the performance behavior of their applications.
Problem statement: Good or Bad performance
So how a good or bad performance of any website or application is judged? Ultimately it is all about perceived response, some crucial applications are expected to deliver output within thresholds of 1 second or less example, bank applications, while for others it is still okay to take a minute or less to attain to user’s request example, shopping, Facebook website. In former case, a delay of few seconds might irritate a user whereas in latter case the user does not care much about the few extra seconds or minutes spent. So precisely, a well-performing application is one that lets the end user carry out a given task without undue perceived delay or irritation. The important fact is that the performance really is in the eye of the beholder [2].
From an end user perspective, it sounds simple, however from organizations perspective which are accountable and need to take care of their applications performance, there is an exigency to translate this very fact into quantifiable output. Different organizations might invent different ways of predicting the response but use of standard Key performance indicators (KPIs) such as end to end response time, cpu time, database time, memory etc should be considered here. These KPIs are measurable and assessable and can tell whether a system or application under test is behaving good or bad by comparing it against some standard thresholds numbers. A gauge of these performance indicators would tell how well (or not) application is providing service to the end user or efficiency-oriented indicators such as throughput and capacity would measure how well (or not) an application makes use of the hosting infrastructure.
Yet these indicative numbers desert to convey the essence of the data to the end-user. The inferences, which are paramount to take important decisions such as, can the software be released to the customers or is it a better competitive product in the market or how well application would perform in near future with increasing user/data etc. are still lagging and cannot be interpreted easily. So there arises a necessity of important statistical inferences to be drawn out of these key performance indicators of test data which would help the organization to take sagacious decisions for any business.
In this paper, I have presented different techniques such as creation of box plot for five-number summary, defining frequency distribution for performance test data, identification of probability distribution for future data-set, building hypothesis tests and conducting regression analysis for performance test data which would help to arrive at statistical inferences from performance kpi numbers.
Creation of box plot for five-number summary of performance test data
A box plot is a graphical summary of test data that is based on a five-number summary minimum, first quartile, median, third quartile and maximum. A quartile divides data into different quarters. The first quartile (Q1) is defined as the middle number between the smallest number and the median of the data set. The second quartile (Q2) is the median of the data. The third quartile (Q3) is the middle value between the median and the highest value of the data set [6]. The first quarter represents lowest 25% of data, the second quarter describes the next 25% of data up to median value, the third quarter specifies higher 25% of data above the median value and the last quarter describes highest 25% data up to the maximum value in test data.
Box plot diagram is effective to eliminate outliers from the test data. It allows to compare different categories of data for easier, effective decision-making. A key to the development of box plot is the computation of the interquartile range, IQR = Q3 – Q1.
Here, I have taken an organization test data for one product area and have recorded key performance indicators values, such as End to end performance time, CPU time and Database time for it.
Computing the five-number summary for the performance data results in:
Minimum
0.1
First Quartile
0.9005
Median
1.491
Third Quartile
2.721
Maximum
48.65466667
Then calculating the Interquartile range, lower limit and upper limit:
Interquartile Range
1.8205
Lower limit
-1.83025
Upper limit
5.45175
Next is to draw the box plot diagram using the above values:
Inferences:
* The complete set of test data can be represented by the five number values
* The central dispersion of end to end response time value lies at 1.491 and 50% of these values lies within range of 0.9005 (first quartile) and 2.721 (third quartile) which indicates half of the time performance of application would fall within these thresholds
* The lower limit and upper limit are at -1.83 and 5.45 respectively which means for an end user, the response time of the application can be as close as to 0.00… seconds in ideal environment (ignoring the negative values for time) or as bad as 5.45 seconds
* The maximum value of 48.65 second is an outlier here since it falls beyond the scope of upper limit value. Similar values such as 14 secs, 16 secs, 25 secs are outliers for given application performance and should be eliminated from the test data in order to eliminate their impact
Defining frequency distribution for performance test data
A frequency distribution is tabular summary of test data showing the number (frequency) of observations in each of several nonoverlapping categories or classes. A frequency distribution is intended to show how many instances there are of each value of a variable. [1]
Using frequency distribution, the organizations can calculate what is the standard performance kpi (response time or cpu time) value under which most applications fall.
We can compute the frequency distribution table first and then chart as defined in below steps:
* Find the range of the data: The range is the difference between the largest and the smallest values [1]
* Determine the number of classes i.e, which data are to be grouped. H.A. Sturges has given a formula to determine the approximation number of classes. It can vary usually from 5 to 20 [1]
K = 1 + 3.322 log N
Where K= Number of Classes, log N = Logarithm of the total number of observations.
For Example: If the total number of observations is 50, the number of classes would be
K=1+3.322log N
K=6.644
* Calculate the approximate class interval size: The size of class interval can be obtained by dividing the range of data by number of classes and denoted by h class interval size [1]
(h)= Range/Number of Classes
* Decide the initial class value [1]
* Compute the remaining class limits: Once the lowest class boundary of the lowest class has been decided, then by adding the class interval size to the lower-class boundary, compute the upper-class boundary. The remaining lower and upper class limits may be determined by adding the class interval size repeatedly till the largest value of the data is observed in the class. [1]
* Distribute the data into respective classes: All the observations are marked into respective classes [1]
Here, I have used excel functions and above steps to calculate the frequency distribution table and chart as below:
Row Labels
Count of End to End Response Time [s]
0-5
953
5-10
37
10-15
6
15-20
6
20-25
2
25-30
1
35-40
2
40-45
1
45-50
1
Inferences:
* Majority of end to end response time values of the application lies below 5 seconds i.e., almost 953 of the values recorded for a product area falls under 5 seconds’ response time threshold
* Only 1 or 2 values at most have peak values such as 11 seconds or 48 seconds. These bare minimum values are the outliers in the performance of the application
* So, with consideration to the above two points the application takes on average the threshold value of 5 seconds to respond for any user interaction step
Identification of probability distribution for future data-set
The probability distribution represents the likelihood of an event occurring in near future.
In contrast to frequency distribution where the diffusion of current data set is measured, the probability distribution table and graph conveys information about the futuristic events. [5]
In business scenario, using probability distribution we can compute the chances of an application, for instance, to perform within the defined threshold limit. It can be used to generate scenario analyses. A scenario analysis method make use of probability distributions to construct several exclusive and distinct possibilities for the outcome of a future event. For example, there can be three identified scenarios for a business: worst-case, probable-case and best-case. The worst-case scenario would contain some value from the lower end of the probability distribution; the probable-case scenario would contain a value from the middle of the distribution; and the best-case scenario would contain a value in the upper end of the scenario. [5]
Risk evaluation could be another beneficial denouement of probability distribution which would help to understand and mitigate the risk for any business.
Assuming the data is normalized, I calculated the probability chart for the performance test data set as below, using excel data analysis functions (NORM.DIST):
Response time threshold (x)
Probability function f(x)
Probability percent
1
0.352803
35.28%
2
0.466035
46.60%
3
0.582105
58.21%
4
0.691394
69.14%
5
0.785915
78.59%
6
0.861006
86.10%
7
0.915801
91.58%
8
0.95253
95.25%
9
0.975143
97.51%
10
0.987931
98.79%
Inferences:
* As per the current readings of the product area, the application will have response time value of 3 seconds in almost 58% of future probable cases. This differs from the frequency distribution chart where 94% of the data have response time of 3 seconds
* Here we can ask questions like what would be the probability for end to end response time value to be 4 seconds or 5 seconds? So, from above chart the probability holds good at 79% for 5 seconds’ criteria of any application performance. This helps in drawing conclusions for a business case or deciding on the future release of an application
* Probability for response time value to fall within 5 seconds and 10 seconds’ thresholds is (0.987931 – 0.785915 = 0.2020) i.e., 20%. Similar extrapolations can be drawn further.
Building hypothesis test
In hypothesis testing we begin by making a tentative assumption about a population parameter. This tentative assumption is called Null hypothesis and is denoted by H0. We then define another hypothesis called the alternative hypothesis, which is the opposite of the statement in null hypothesis. The alternative hypothesis is denoted by Ha. [7]
The hypothesis testing procedure uses data from a sample to test the two competing statements indicated by H0 and Ha [7]. The p-value is then calculated using mean, hypothesized mean and standard error and this p-value is compared against the alpha or the significance level using the below rule:
Rule
p-valuealpha
Fail to reject Null hypothesis
In the current data sets, I took a sample of data from the current population and assumed that the Database CPU time would fall within threshold of 0.11 seconds for the application. So, writing this statement in Null hypothesis form and opposite statement in alternative hypothesis form:
H0: Database CPU time 0.11 seconds
Null Hypothesis: H0
0.11
Alternative hypothesis: H1
Greater than 0.11 seconds
Mean
0.101435169
SD
0.190488405
Sample size
350
Standard error
0.01
Confidence coefficient
0.95
Alpha
0.05
Test statistics (t)
-0.8411710
Lower limit
0.1185648
Upper limit
0.1014352
p-value
0.799585942
Fail to reject H0 at
0.11 seconds
Not significant
So as per the rule, I fail to reject null hypothesis and conclude that database time falls within threshold of 0.11 seconds for the dataset. Similarly, I made different assumption that the database time would fall within threshold of 0.08 seconds. However, this time the null hypothesis is rejected based on the below computations as p-value came out to be smaller than alpha value. This value was significant enough to reject the claim.
Null Hypothesis: H0
0.08
Alternative hypothesis: H1
> 0.08 seconds
Mean
0.101435169
SD
0.190488405
Sample size
350
Standard error
0.01
Confidence coefficient
0.95
Alpha
0.05
Test statistics (t)
2.1051953
Lower limit
0.0585648
Upper limit
0.1014352
p-value
0.017994292
Reject H0 at
0.08 seconds
Significant
Conducting regression analysis
Organizational decisions are often based on the relationship between two or more variables. For example, after predicting the relationship between advertising expenditures and sale, a marketing manager might attempt to predict sales. Sometimes this relationship would be built based on past experiences or sometimes solely on the intuition of the management [7]
However, a more accurate method called Regression analysis can be employed to develop an equation between two or multiple variables and to show how they are related. In regression technology, the variable being predicted is called dependent variable and the variable or variables being used to predict the value of the dependent variable are called Independent variables. Depending on the number of independent variables used, we term the regression analysis as Simple linear regression (one-variable) or Multiple regression (two or more variables).[7]
Here, I have applied linear regression on variables End to end response time and Database time and tried to predict the relationship between them using Excel data analysis functions:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.872201
R Square
0.760734
Adjusted R Square
0.756536
Standard Error
1.451801
Observations
59
ANOVA
df
SS
MS
F
Significance F
Regression
1
381.9804
381.9804
181.2287
2.38E-19
Residual
57
120.1403
2.107725
Total
58
502.1207
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
1.473333
0.219121
6.723849
9.17E-09
1.034552
1.912115
1.034552
1.912115
X Variable 1
1.042476
0.077438
13.46212
2.38E-19
0.88741
1.197543
0.88741
1.197543
From the analysis table above, the relationship between two variables is envisioned as:
Y = 1.0425 x + 1.4733
i.e., in the form of Y= mx+ c
The correctness of these coefficient values can be determined by p-value in the regression chart. The p-value of 9.17E-09 and 2.38E-19 for intercept and x-variable coefficient respectively, are extremely low and thus can be interpreted as highly accurate.
Multiple R is the correlation coefficient and its value determined was 87%, which indicates that the dependent variable response time is strongly related to independent variable database time.
R square is the coefficient of determination which states that 76% of the variance in response time can be attributed to database time. It is a statistical measure of how close the data are to the fitted regression line.
The Anova highlights some key figures:
Degree of freedom (no of independent variable used) which is 1 for regression, 57 for Residual (n-k-1) and Total 58 (n-1),
Sum of Squares of Regression values, mean sum of squares and F- statistics significance value.
The F-statistics value which is very low in this case means regression analysis is good.
The residual plot and probability plot between response time and database time is plotted as below:
Citations/References:
[1] http://www.emathzone.com/tutorials/basic-statistics/construction-of-frequency-distribution.html
[2] https://www.safaribooksonline.com/library/view/the-art-of/9781491900536/ch01.html
[3] https://abstracta.us/2015/10/12/why-performance-testing-is-necessary/
[4] https://loadstorm.com/2012/06/why-performance-testing-important-perspective-guest-blogger/
[5] http://smallbusiness.chron.com/role-probability-distribution-business-management-26268.html
[6] https://www.quora.com/Is-median-the-same-with-second-quartile
[7] Book on Statistics for Business and Economics (by Anderson, Sweeny, Williams, Camm, Cochran)
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