# Standard Error Multiply

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## What Happens To Standard Deviation When You Multiply

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## How Does Multiplication Affect Standard Deviation

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## Standard Error Propagation

with the deviations? up vote 0 down vote favorite If I multiply the averages of two sets of data, then what can I conclude with the deviation of that data? That is, for a given average X1 and X2, both are different sets of data but related, I calculated a derived average X3 = X1 * X2. Both X1 and X2 also has their own standard deviation values, D1 and D2. How can I calculate the combining standard deviations standard deviation value D3? My concrete sample problem to illustrate the use-case I have sample performance measurements of a computer operation, measured in miliseconds / invocation (the first data set) and invocations / day (the second data set). Both of these has a mean and a standard deviation value. I would like to get another measure that is in miliseconds / day. So I multiplied the first data with the second : X1 * X2 = X3 miliseconds / invocation * invocations / day = miliseconds / day The question is, how do I get the standard deviation value of X3 ? Thanks in advance. statistics standard-deviation share|cite|improve this question asked Mar 8 '12 at 3:18 adib 10314 One could make a calculation assuming independence. But the independence assumption may be too crude to make the result reliable. –André Nicolas Mar 8 '12 at 3:44 Is it independent? These two data sets measure the same operation. –adib Mar 8 '12 at 3:47 Certainly not independent. But independence assumption may give a ballpark estimate. –André Nicolas Mar 8 '12 at 3:56 add a comment| 1 Answer 1 active oldest votes up vote 2 down vote accepted Assuming $X_1$ and $X_2$ are independent, $$\text{Var}(X_1 X_2) = \text{Var}(X_1) \text{Var}(X_2) + E[X_1]^2 \text{Var}(X_2) + E[X_2]^2 \text{Var}(X_1)$$ EDIT: Without that assumption, $$\text{Var}(X_1 X_2) =

error of means Tweet Welcome to Talk Stats! Join the discussion today by registering your FREE account. Membership benefits: • Get your questions answered by averaging standard deviations community gurus and expert researchers. • Exchange your learning and research experience error propagation multiplication among peers and get advice and insight. Join Today! + Reply to Thread Results 1 to 6 of adding standard deviations 6 Thread: multiplying Standard error of means Thread Tools Show Printable Version Email this Page… Subscribe to this Thread… Display Linear Mode Switch to Hybrid Mode Switch to Threaded Mode 03-23-201110:29 http://math.stackexchange.com/questions/117763/multiplying-two-averages-what-to-do-with-the-deviations AM #1 frymor View Profile View Forum Posts Give Away Points Posts 3 Thanks 0 Thanked 0 Times in 0 Posts multiplying Standard error of means Hi guys, I am new here (and also to statistics ). I have a data set of many measurements. For each one of them I calculated the mean and the SD (deviation). From that I http://www.talkstats.com/showthread.php/16947-multiplying-Standard-error-of-means calculated separately for each of the data set a SEM. Now I would like to multiply, divide add and subtract this data samples from/with each other. Doing so for the actual values is quite trivial, but what do I do with the SEM-values. How do this SEM Values changed according the applied calculation? Example( with data from the internet): set 1: 46,42,44,45,43 => mean 44 ; SD= 1.6 ==> SEM : 1.6 set 2: 52,80,22,30,36 => mean 44 ; SD = 22.9 ==> SEM : 10.3 What do I do with the two sets if I want to combine them together? I would appreciate any help I can get. Thanks Assa Reply With Quote 03-23-201101:02 PM #2 SPR View Profile View Forum Posts Posts 156 Thanks 0 Thanked 2 Times in 2 Posts Re: multiplying Standard error of means Hello Frymor, I do not fully understand what do you mean by doing arithmetic with samples. For example, addition could be considered as combining data from both samples having one with double number of observations or adding paired observations of two s

or more quantities, each with their individual uncertainties, and then combine the information from these quantities in order to come up with a final result of our experiment. How can you state your answer for the combined result of these measurements and their uncertainties scientifically? The answer to this fairly common question depends on how http://lectureonline.cl.msu.edu/~mmp/labs/error/e2.htm the individual measurements are combined in the result. We will treat each case separately: Addition of measured quantities http://www.healthknowledge.org.uk/e-learning/statistical-methods/practitioners/standard-error-confidence-intervals If you have measured values for the quantities X, Y, and Z, with uncertainties dX, dY, and dZ, and your final result, R, is the sum or difference of these quantities, then the uncertainty dR is: Here the upper equation is an approximation that can also serve as an upper bound for the error. Please note that the rule is the same for addition and subtraction of quantities. standard deviation Example: Suppose we have measured the starting position as x1 = 9.3+-0.2 m and the finishing position as x2 = 14.4+-0.3 m. Then the displacement is: Dx = x2-x1 = 14.4 m - 9.3 m = 5.1 m and the error in the displacement is: (0.22 + 0.32)1/2 m = 0.36 m Multiplication of measured quantities In the same way as for sums and differences, we can also state the result for the case of multiplication and division: Again the upper line is an approximation and standard error multiply the lower line is the exact result for independent random uncertainties in the individual variables. And again please note that for the purpose of error calculation there is no difference between multiplication and division. Example: We have measured a displacement of x = 5.1+-0.4 m during a time of t = 0.4+-0.1 s. What is the average velocity and the error in the average velocity? v = x / t = 5.1 m / 0.4 s = 12.75 m/s and the uncertainty in the velocity is: dv = |v| [ (dx/x)2 + (dt/t)2 ]1/2 = 12.75 m/s [(0.4/5.1)2 + (0.1/0.4)2]1/2 = 3.34 m/s Multiplication with a constant What if you have measured the uncertainty in an observable X, and you need to multiply it with a constant that is known exactly? What is the error then? This is easy: just multiply the error in X with the absolute value of the constant, and this will give you the error in R: If you compare this to the above rule for multiplication of two quantities, you see that this is just the special case of that rule for the uncertainty in c, dc = 0. Example: If an object is realeased from rest and is in free fall, and if you measure the velocity of this object at some point to be v = - 3.8+-0.3 m/s, how long has it been in free fall? Answer: we can calculate the time as (g = 9.81 m/s2 is assumed to be known exactly) t = - v

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Standard Error p the mean account for and three standard deviations account for Prediction interval on the y-axis given from the standard score on the x-axis The - - rule y-axis is logarithmically scaled but the values on it are not modified p Standard Deviations p In statistics the rule is a shorthand used to remember the percentage of values that lie within p Standard Deviation Percentage Calculator p a band around the mean in a normal distribution with a width of one two and three standard deviations respectively more accurately and of the values lie within p One Standard

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Standard Deviation Error Bar p error or uncertainty in a reported measurement They give a general idea of how precise a measurement is or conversely how far from the reported value the true error free value might be Error bars often represent one standard deviation of uncertainty one standard error or a certain confidence interval e g a interval These quantities are not the same and so the measure selected should be stated explicitly in the graph or supporting text Error bars can be used to compare visually two quantities if various other conditions hold This can determine whether differences

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Standard Error In Marketing Research p Newletter Job Center Add Profile to directory Marketing programs How to Interpret Standard Deviation and Standard Error in Survey Research Posted January DataStar Inc Article Standard Deviation and Standard Error are perhaps the two least understood p How To Write Standard Deviation In A Report p statistics commonly shown in data tables The following article is intended to explain their how to know if standard deviation is high or low meaning and provide additional insight on how they are used in data analysis Standard Deviation and Standard Error are perhaps p How To Write

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Standard Error Anova p standard deviations and standard errors Greg Samsa SubscribeSubscribedUnsubscribe Loading Loading Working Add to Want to watch this again later Sign in to add this video to a p Standard Error Anova Formula p playlist Sign in Share More Report Need to report the video anova standard deviation assumption Sign in to report inappropriate content Sign in Transcript Statistics views Like this video standard error of estimate anova table Sign in to make your opinion count Sign in Don't like this video Sign in to make your opinion count Sign in Loading Loading Transcript p Anova Standard

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Standard Error Graphpad Prism p OF p When To Use Standard Deviation Vs Standard Error p STATISTICS Standard Deviation and Standard Error of the Mean Dear GraphPad Standard Deviation and Standard standard deviation vs standard deviation of the mean Error of the Mean Rather than show raw data many scientists present results as mean plus or minus the standard deviation SD or standard error SEM This section helps you understand what these values mean URL of this page http www graphpad com support stat standard deviation and standar htm - GraphPad Software Inc All rights reserved p p Graphpad com

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Standard Error Mean Graphpad Prism p Graphpad com FAQs Find ANY word Find ALL words Find EXACT phrase Why does Prism report the standard error for logEC but not for the EC itself when it fits dose-response curves FAQ Last Modified convert standard error to standard deviation -January- See this long answer or read on for a shorter answer If as standard error and standard deviation difference is typical your doses are equally spaced on a LOG scale then the uncertainty of the IC or EC is standard deviation of the mean excel symmetrical on a LOG scale In this

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Standard Error Of Mean Graphpad p Graphpad com FAQs Find ANY word Find ALL words Find EXACT phrase The standard error of the difference between two means FAQ Last Modified -May- As part of the results of an unpaired convert standard error to standard deviation t test Prism reports the standard error and confidence interval for the standard error and standard deviation difference difference between two means The row labeled 'difference between means' shows just that The difference between the mean of p Standard Deviation Of The Mean Excel p group A and the mean of group B It also

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Standard Error Of A Ratio p Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of error ratio formula this site About Us Learn more about Stack Overflow the company Business Learn p Variance Of A Ratio p more about hiring developers or posting ads with us Cross Validated Questions Tags Users Badges Unanswered Ask Question standard deviation of a ratio of independent variables Cross Validated is a question and answer site for people interested in statistics machine learning data analysis data mining

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Standard Error Mean Graphpad p OF p When To Use Standard Deviation Vs Standard Error p STATISTICS Standard Deviation and Standard Error of the Mean Dear GraphPad Standard Deviation and Standard standard deviation vs standard deviation of the mean Error of the Mean Rather than show raw data many scientists present results as mean plus or minus the standard deviation SD or standard error SEM This section helps you understand what these values mean URL of this page http www graphpad com support stat standard deviation and standar htm - GraphPad Software Inc All rights reserved p p Graphpad com

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Standard Error Command In Matlab p Search All Support Resources Support Documentation MathWorks Search MathWorks com MathWorks Documentation Support Documentation Toggle navigation Trial Software Product Updates Documentation Home MATLAB Examples matlab plot standard deviation Functions Release Notes PDF Documentation Data Import and Analysis Descriptive Statistics p Matlab Standard Deviation Of Matrix p MATLAB Functions std On this page Syntax Description Examples Standard Deviation of Matrix Columns Standard Deviation of -D p Variance In Matlab p Array Specify Standard Deviation Weights Standard Deviation Along Matrix Rows Standard Deviation Excluding NaN Input Arguments A w dim nanflag More About Standard Deviation Tall

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Standard Error Of Product p measurements on two variables are reproduced from a paper by H Ku Ku The p Standard Deviation Of Two Independent Variables p reported value Y is a function of averages of standard deviation of two variables in excel N measurements on two variables Function Y of bar X standard deviation two variables calculator bar Z bar X and bar Z are averages of N measurements CENTER B Standard deviation of Y s x standard p Standard Deviation Of Product Of Random Variables p deviation of X s z standard deviation of Z s xz covariance

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Standard Deviation Maximum Error p maximum error of the estimate is given by the formula for E shown The Z here is the z-score obtained from the normal table or the bottom of the t-table as explained in the introduction to estimation The z-score is p Standard Error Of The Mean p a factor of the level of confidence so you may get in the habit of writing standard error formula it next to the level of confidence Once you have computed E I suggest you save it to the memory on your calculator p Standard Deviation Of The Mean

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Standard Error Numbers Mac p Numbers for Mac Browse all functions by category Date Time Duration Engineering Financial Logical Information standard deviation symbol on mac Numeric Reference Statistical Text Trigonometric Date standard deviation numbers meaning Time DATE Combines separate values for year month and day and returns a date time value DATEIF Returns p How To Calculate Standard Error In Excel p the number of days months or years between two dates DATEVALUE Converts a date text string and returns a date time value This function is provided for compatibility with other p Standard Error Vs Standard Deviation p spreadsheet

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Standard Error Of The Mean Significant Figures p standard deviation in Section you know that your calculator actually doesn't give the answer for sigma as standard deviation significant figures sec but rather img There are significant digits in this sig figs for mean and standard deviation number Significant digits are the digits remaining after one ignores leading zeros If we kept all of them p Standard Deviation Percent Error p our final answer for the oscillation period would be img The above result implies that we measured T with a precision of better than a billionth of a second with

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Standard Error Outliers p outliers in the middle column as well as one outlier in the first column In statistics an outlier is an observation point that is distant from other observations An outlier may be due to variability in the measurement or it p Absolute Deviation Around The Median p may indicate experimental error the latter are sometimes excluded from the data set Outliers using standard deviation to find outliers in excel can occur by chance in any distribution but they often indicate either measurement error or that the population has a heavy-tailed distribution In p Standard Deviation Outlier

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Standard Error Sigma Hat p See also rule Cumulative probability of a normal distribution with expected value and standard deviation In statistics the standard deviation SD also represented by the Greek letter sigma or the Latin standard deviation symbol letter s is a measure that is used to quantify the amount of variation p Standard Error Formula p or dispersion of a set of data values A low standard deviation indicates that the data points tend to be close population standard deviation to the mean also called the expected value of the set while a high standard deviation indicates that

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Standard Error Graphpad p OF p When To Use Standard Deviation Vs Standard Error p STATISTICS Standard Deviation and Standard Error of the Mean Dear GraphPad Standard Deviation and Standard standard deviation vs standard deviation of the mean Error of the Mean Rather than show raw data many scientists present results as mean plus or minus the standard deviation SD or standard error SEM This section helps you understand what these values mean URL of this page http www graphpad com support stat standard deviation and standar htm - GraphPad Software Inc All rights reserved p p Graphpad com FAQs

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Standard Error Plus Minus Mean p a choice of exactly two possible values one of which is the negation of the other In experimental sciences the sign commonly indicates the confidence interval or error in a measurement often the standard deviation or standard p Mean Plus Or Minus Standard Deviation Excel p error The sign may also represent an inclusive range of values that a reading plus or minus standard deviation or standard error might have In engineering the sign indicates the tolerance which is the range of values that are considered to be acceptable p Mean Plus Minus Standard

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Standard Error Significant Digits p as or or This page will give you some guidance on how to report your experimental results with the standard deviation significant appropriate number of significant digits When documenting experimental data it is important how many significant figures for mean not to state the data with too much precision That is the number of significant digits should reflect how many sig figs for relative standard deviation the level of experimental uncertainty How do you know what the level of experimental uncertainty and therefore the precision of your measurements is The best way is to take