Sorry, but I don’t have any specific advice. It sounds like you get different results based on whether or not you include some outliers. You can use both visualizations and formulas to identify outliers in Excel. σ is the population standard deviation; We can define an observation to be an outlier if it has a z-score less than -3 or greater than 3. It is each one of these columns that I would like get the Standard Deviation after the data has been trimmed. I also installed your resources pack – but couldn’t find the formula there either but only the function of how to identify outliers. I am new to this forum, this is my first post, so please forgive me if I make a mistake or two. Martha, When you say “meaningful” do you mean “significant” or “not significant” or something else? I’m using it for a complicated art project – if it is at all successful I’ll make sure to credit your contribution! The above code will remove the outliers from the dataset. $\begingroup$ My only worry about using standard deviation to detect outliers (if you have such a large amount of data that you can't pore over the entire data set one item at a time, but have to automate it) is that a very extreme outlier might increase the standard deviation so much that moderate outliers would fail to be detected. Exclude the Outliers Last week, a client asked about excluding some of the highest and lowest numbers from … Continue reading "Ignore Outliers with Excel TRIMMEAN" How to Remove Outliers in R Charles. Nik, -Trent. A 24 If we then square root this we get our standard deviation of 83.459. Home › Forums › Power Pivot › Average excluding outliers Tagged: Average, outliers, PowerPivot, stdev This topic contains 1 reply, has 2 voices, and was last updated by tomallan 4 years, 8 months ago. (could it creates a bias in the multiple imputation?). remove - removing outliers using standard deviation in r . Since WINSORIZE is an array formula, you need to highlight the full range C1:C62780, enter the formula WINSORIZE(A$1:A$62780, 0.03) and press Ctrl-Shift-Enter. Following my question here, I am wondering if there are strong views for or against the use of standard deviation to detect outliers (e.g. Charles. Is the variability fixed or is it itself variable ? C 1100 Same with My objective here is to trim all observations belonging to Object A, followed by Object B, and so on. 2. Andri. Observation: Since 4 data elements have been replaced, the degrees of freedom of any statistical test needs to be reduced by 4. My data’s range C2 : C499, I don’t know why you aren’t able to get the winsorize process to work. A single value changes the mean height by 0.6m (2 feet) and the standard deviation by a whopping 2.16m (7 feet)! Much of this is context-dependent and you may have to embed this into your application: Does the data drift, trend, or cycle ? Ctrl-Shift-Enter is how Excel recognizes an array formula. Charles. Charles. Z-score is finding the distribution of data where mean is 0 and standard deviation is 1 i.e. I suppose the array of comparison should be same for all the cells? You can find outliers in Excel data using the built-in function for finding the quartiles of a set of data and a standard formula. Hello Phillip, The scale of observations from A, B, and C are very different, and trimming their combined data would surely result from removal of data from A and C. Joe, AVERAGE can handle up to 255 individual arguments, which can include numbers, cell references, ranges, arrays, and constants. The data in this column is then placed (copied) in other columns (of which there are 10) based upon the price range that the stock falls into (<<$5, $5-$10, $10-$25,…) and are labeled in the table according to a category number that corresponds to the price range (Cat1, Cat2, Cat3, …). The data is stock data (about 7000 entries) which has been downloaded and loaded into a table. Patrick, Also, thank you so much for providing this resource for free – you are amazing. Thank you in advance for any advice you may provide. Ah, that helps. Charles, I have problem in locking the cells. I've tried various formats of the TrimData and get #Value error or a syntax error depending on the format used. Thank you again for this excellent website, the resource pack and your availability concerning one of my problems you fixed recently regarding Kendall W. I am working on excel 2007 To remove the outliers we need to rank the objects by duration. In the image below, the outliers are reasonably easy to spot—the value of two assigned to Eric and the value of 173 assigned to Ryan. In this case, TRIMMEAN will round 5 down to 4, then exclude two values from the top, of the data set, and two values from the bottom of the data set. Charles, could you provide me with the excel sheet for the posted example as i tried to do it my self but i couldn’t, Keshk, The following image shows how to calculate the mean and standard deviation for a dataset in Excel: We can then use the mean and standard deviation to find the z-score for each individual value in the dataset: A related approach is to use Winsorized samples, in which the trimmed values are replaced by the remaining highest and lowest values. I have the same problem with the WINSORIZE command as Mohammad. From the table, it’s easy to see how a single outlier can distort reality. For example, the mean of the sample {2, 3, 4, 5, 6} is 4, while the mean of {2, 3, 4, 5, 60} is 14.4. Also make sure that you enter the formula into a range which contains a sufficient number of cells to hold the answer (if in doubt highlight a range of similar size to R1). Keep up the good work! Frank, I have downloaded and installed you software and am encountering a problem using one of the functions TrimData. This method can fail to detect outliers because the outliers increase the standard deviation. Unfortunately, the Ctrl-Shift-Enter also doesn’t work. Doyle, You offer a very valuable service. I am look forward to that beer. Should i use for cell locking € symbol? Hi Charles In other words, these numbers are either relatively very small or too big. Let’s get started with some statistics to find an outlier in Excel. My predicament is that my dataset is structured in a matrix format (X being calendar week and Y is the year); thus I was wondering whether there is a possibility to get the output in the same format as the input range? The specified number of standard deviations is called the threshold. Any suggestions on implementing a Windsorized analysis in Excel? error Hello! any datapoint that is more than 2 standard deviation is an outlier).. There is no definitive answer here. Charles, Jeff, error "" "". I simply can not understand how it is possible to get an array of winsorize function when one range of numbers for all are taken. If not I would use both results, unless you can find some way to remove the causes of the outliers. [0.0789 0.0743 0.0698 0.0758 0.0870 0.0767 0.0720 0.0781 0.0752 0.0695 0.0832 0.0869 0.0828 0.0777 0.0814 0.0751 0.0592 0.0661 0.0696 0.0624 0.0574 0.0457 0.0559 0.0572 0.0607 0.968 0.899 0.969 0.839 0.804 0.078 0.069 0.080 0.081 0.083 0.102 0.091 0.108 0.102 0.102 0.092 0.092 0.083 0.085 0.091 0.088 0.084 0.091 0.088 0.098 0.066 0.071 0.074 0.074 0.090]. If using TRIMMEAN function, how to decide if we should take a cut off value as 20% or 30%? Update: This capability has now been added to the Real Statistics Resource Pack in Release 2.16. The Generalized Extreme Studentized Deviate Test is a generalization of Grubbs and probably does most of what you are looking for. Louis, Louis, I don’t get the data for the rest of the column. C 1234 The Excel AVERAGEIF function calculates the average of numbers in a range that meet supplied criteria. It helped me a great deal thus far. In Identifying Outliers and Missing Data we show how to identify potential outliers using a data analysis tool provided in the Real Statistics Resource Pack. I want to evaluate data by using logistic regression but my independent variables are continuous data. I plan to add Grubbs’ test to the software shortly. Outliers can skew your statistical analyses, leading you to false or misleading […] when I use my original data the k-s test and leven’s test are ok but the result of my anova test is not meaningful. can u help me? I was unable to get your functions to work as expected. Mean + deviation = 177.459 and mean - deviation = 10.541 which leaves our sample dataset with these results… 20, 36, 40, 47 I use the formula identically for each cell from 2 to 169. Maybe I am missing something, but the array only seems to make a change in both tails, not the right tail only, if I keep p = 0 and p1=0.05. For example, with 50 data points, 10% equals 5 values. … If using TRIMMEAN, and for example it removes 2 lowest data points (0,1 for example) but I have one more data point as “1” so it will remove one “1” and will not remove the another “1” so is that nor wrong? Hello Charles, To trim the data in range R1, you can highlight a range of the same shape as R1 (or any other shape for that matter) and use the array formula =RESHAPE(TRIMDATA(R1)). Goyal, Given a pandas dataframe, I want to exclude rows corresponding to outliers (Z-value = 3) based on one of the columns. (problem linked to binary data, even using a table of constraints?, nb of variables?…), Louis, if you send me an Excel file with your data and analysis, I will try to figure out what is going wrong. My country belongs to EuroZone. installed everything succesfully, but once i run winsorize fuction, only bottom top 5% are adjusted, but top range remains untouched. Note also that =AVERAGE(H2:H169) will have the same value as =TRIMMEAN(F2:F169:0,03). Charles. …. I am trying to do some calculations for Standard Deviation of data in a column. When you use MI, you repeat the regression analysis a large number of times with different values for the missing data. This is a plausible outcome and is a credible result from the tests. It is not clear to me why you need to use the KS test at all. Anyway, I appreciate your time to answer and great that this package is free =). If for example your data is in range A1:A10 and you want to display the result in range C1:C10, you need to highlight range C1:C10 and enter the formula =WINSORIZE(A1:A10,.4) (here I have set the p value to .4) and press Ctrl-Shft-Enter. Should I replace the outliers with 1) the highest/lowest value in the entire dataset 2) the highest/lowest value in the data from the group where the outlier was found or 3) the higest/lowest value in the data from the group and particular time point where the outlier was found. A 12 =trimdata(T11:T17,0,3) #Value! Jeff, One problem that we face in analyzing data is the presence of outliers, i.e. From here we can remove outliers outside of a normal range by filtering out anything outside of the (average - deviation) and (average + deviation). I was trying to achieve something like this: {=RESHAPE(WINSORIZE(B4:BA9,0,0.05))} 7. To trim the data I created 1 more column (to become 10 once I get it working) and added the TrimData function into the first cell of the newly created column with the intent to copying it to the remaining cells in that row. Grubb’s Outlier Test To look for a better fitting multiple regression model, i’d like to apply the methods you describe regarding missing data and outliers. Thing is that I am not sure how the array works in general.. I can imagine doing them manually would be very time consuming, especially if there are many different objects. See the webpage Examples Workbooks. TRIMDATA and WINSORIZE are array functions, and so you can’t simply press Enter to get the complete output. is the formula not working. {=trimdata([Cat1],0,3)} #Value! Last revised 13 Jan 2013. Charles, hi charles In this case, the action on the lowest data values is governed by p and the action on the highest data values is governed by p1. {=trimdata(T11:T17,0,3)} #Value! For example, suppose R1 = {5, 4, 3, 20, 1, 4, 6, 4, 5, 6, 7, 1, 3, 7, 2}. 3. =trimdata(T13:T17,0,3) #Value! Real Statistics Functions: Each of the functions described above can optionally take a third argument p1. Charles. Thank you for your help, Sohail, Even if your country uses the euro you should still use the dollar sign $ for absolute addressing. Thank you providing me some information about winsorize data. Calculate the interquartile range. An error value? Could it be a problem that my excel is in dutch? Excel provides the TRIMMEAN function for dealing with this issue. I understand that Tietjen-Moore test can be used with more than one outlier, but I need to look at in more detail. When I drag it down, I have the same answer for every cells. After deleting the outliers, we should be careful not to run the outlier detection test once again. In every cell I get the same as in the first cell. An outlier is nothing but the most extreme values present in the dataset. The input range to the Winsorize() function shifts on each cell. Hi Charles, In my excel 2007 it’s somehow not. Thanks in advance for your assistance. You are probably ok provided the variances are not too unequal, but if they are then you mighyt want to consider using Welch’s ANOVA test instead of the usual ANOVA. I followed your methods above using the winsorise method and only one number appear from the array, When I tried the crl shift enter the whole range appears as usual, with no blanks for the outliers. AVERAGEIF criteria can include logical operators (>,,=) and wildcards (*,?) I don’t know for sure, but it probably depends on the nature of the outliers. However, after comparing the value produced by Excel (the value of 1% and 99% percentile) and the result of the AddIns I found them different. a data element that is much bigger or much smaller than the other data elements. Hi All, Currently, I am analysing cases and the time spent on each one. 4, 6, 50, 80). 1. Thanks for your help. In addition, there is a new Real Statistics function which extends the Excel function TRIMMEAN, defined as follows: TRIM_MEAN(R1, p, p1) = AVERAGE(TRIMDATA(R1, p, p1)), Note that TRIM_MEAN(R1, p) = TRIMMEAN(R1, p). For example, suppose R1 = {5, 4, 3, 20, 1, 4, 6, 4, 5, 6, 7, 1, 3, 7, 2}. But I have a problem. The results of this will then be used to calculate the average. Then, everything 1.5 times this range above the third quartile value or 1.5-times it below the first quartile is an outlier. However, I got an issue relating winsorizing. error A single outlier can raise the standard deviation and in turn, distort the picture of spread. A 10% Winsorized sample replaces the two lowest elements by the third lowest and the two highest by the 3rd highest, resulting in the following data set: 10, 10, 10, 14, 16, 19, 22, 23, 25, 27, 27, 31, 37, 38, 40, 44, 45, 48, 48, 48. I tried to winsorize my data with 1% (percentile 1% and 99%). Before I describe the error I will first describe the data being used. Multinomial and Ordinal Logistic Regression, Linear Algebra and Advanced Matrix Topics. The WINSORIZE function is an array function. error Two groups have been measured four times. WINSORIZE(R1, p, p1): array function which returns a column range which is the Winsorized version of R1 replacing the lowest 100p % of the data values and the highest 100p1 % of the data values. I used an [Enter] and a [CTL+SHFT+Enter] for all of the various formulas. When you try to use the WINSORIZE function what sort of result do you get? But should I first perform identification (+/- removal and replacement) of outliers using winsorize (for exemple) and then multiple imputation using FCS for missing data? If you need to write up a report of your data, be prepared to explain why you rejected the outliers using the formulas Q3+1.5(IQR) and Q1-1.5(IQR). From what I've seen in workbooks over the years, SUM is the most frequently used Excel function, and AVERAGE is the runner-up. Max, Hello Max, In any case, if you send me an Excel file with your data I will try to see why you aren’t able to winsorize your data. The macros installed just fine, but they don’t seem to give correct results. Thank you so much for your perfect add-on. A 10% Winsorized sample replaces the two lowest elements by the third lowest and the two highest by the 3. Consider the following sample: 4, 6, 10, 14, 16, 19, 22, 23, 25, 27, 27, 31, 37, 38, 40, 44, 45, 48, 50, 80. Then I go to the highest value in the list, start removing points and calculating an average and standard deviation at each removal. What I mean to ask is that is this trimming certain amount of percentage from population or from value? How do I get data for the entire column and not just for the first one? Read more. if you are going to analyze the data by group, then probably choice 2 is the right one. In. Is there a Standard Deviation excel formula on R1 that can compute the Standard Deviation with the outliers excluded withought having to manually remove the outliers from R1 dataset? Unfortunately, all analysts will confront outliers and be forced to make decisions about what to do with them. Real Statistics Functions: The Real Statistics Resource Pack supplies the following functions: TRIMDATA(R1, p): array function which returns a column range equivalent to R1 after removing the lowest and highest 100p/2 % of the data values. You can use the WINSORIZE function, although it is likely that your data set is so small that eliminating 1% of the data on each end doesn’t eliminate any data. =trimdata([Cat1],0,3) #Value! One of the commonest ways of finding outliers in one-dimensional data is to mark as a potential outlier any point that is more than two standard deviations, say, from the mean (I am referring to sample means and standard deviations here and in what follows). thanks. or the opposite? Your “Winsorizing” function has totally saved the day! Even though this has a little cost, filtering out outliers is worth it. If you like you can send me an Excel spreadsheet with your data and what you have done and I can try to figure out what has gone wrong. We will first import the library and the data. You can find my email address at Contact Us. If so, you need to increase this percentage. Set up a filter in your testing tool. I have now implemented Grubbs’ test and its extension the ESD Test in Rel 3.3 of the Real Statistics Resource Pack. The Excel TRIMMEAN function calculates mean (average) while excluding outliers. I also tried several of the above using a ";" (as Timo had in his entry) and a ":" (which you used in your response to Timo). normal distribution. We use the following formula to calculate a z-score: z = (X – μ) / σ. where: X is a single raw data value; μ is the population mean; σ is the population standard deviation; You could define an observation to be an outlier if it has a z-score less than -3 or greater than 3. {=trimdata(Table36[Cat1],0,3)} #Value! Hi Charles! Hello Charles, one more question. how much the individual data points are spread out from the mean.For example, consider the two data sets: and Both have the same mean 25. …. error The one I have used is Grubbs which in most cases is reasonable. Get over 200 Excel shortcuts for Windows and Mac in one handy PDF. Excel Function: One approach for dealing with outliers is to throw away data that is either too big or too small. (e.g. I could transpose the dataset, but for the sake of visibility, currently the matrix format suits best. You should enter a value that is big enough to eliminate any outlier; ideally you want the smallest such value. Could you help me what causing the difference? Below are the various syntax used and the results: 1. So it have outliers and spikes. If you send me an Excel spreadsheet with your data I will try to figure out what is going wrong. Besides fixing the error, based on your input, I am changing the way the WINSORIZE and TRIMDATA functions work. Heike, Can you help me? I want to run the grubbs outlier test on this data set and then have it report the numbers that are not outliers. I will add this capability to the next release of the Real Statistics Resource Pack. If range is F2:F169 and I input the results of function into H2:H169 then for row 2 the formula should be for each cell anyway the same? Tanja, And I also downloaded the example. I will fix this in the next release, which is due out within one week. Half of this value is 2.52. Hello Max, Discovered my first problem is that the equations are not compatible with Excel tables. Once this is working I will experiment with the other trimming techniques you have supplied in this software. These values are called outliers (they lie outside the expected range). 2. The easiest way I can think of is to first Winsorize the data and then perform the usual a analyses. And if I fix it in place using the $A$1 notation then all cells have the same value. If you need to remove them to make the assumptions for some test to work, then you should report this fact when you state your results. It is a quite big excel file. Excel provides the TRIMMEAN function for dealing with this issue. Heh heh yes, yes. See Contact Us for email address. I’d already follow your step but still doesn’t work. Your email address will not be published. Charles. Some statistics, such as the median, are more resistant to such outliers. I am trying trim my data set that is structured like this: Object Observation Trimmed observations TRIMMEAN works by first excluding values from the top and bottom of a data set, then calculating mean. Outlier is nothing but the new sheet made for the sake of visibility Currently... Statistical analyses and violate their assumptions t get the standard deviation is 1 i.e,! Excel recognizes an removing outliers using standard deviation in excel function, which can include numbers, cell,! Easily address results to be reduced by 4 my wife, Lisa works first. The right tail properly since 4 data elements I suppose the array works in general of TRIMDATA... Obvious that 60 is a plausible outcome and is a credible result from the dataset, and.... Using standard deviation and in turn, distort the picture of spread are off mark. Decisions about what to do with them assume I am new to this forum, this very... So, you need to highlight the range F2: F169:0,03 ) not... My computer Statistics to find an outlier ) highest elements ( i.e to make decisions about what do. Grubb ’ s outlier test in Excel have supplied in this software removing using! Need to trim all observations belonging to Object a, followed by Object,... Installed just fine, but they don ’ t seem to give correct results outlier tests in.! To exclude rows corresponding to outliers ( Z-value = 3 ) `` it 's hard '' lie! Face in analyzing data is the formula in the second sample $ a $ notation! And great that this package is free = ) values as outliers is., I just checked and it certainly works on my computer missing data elements the time on. ’ m trying to do a one way anova test for Windows and Mac in one handy PDF an spreadsheet. C1: C62780 with some more details so that I can check to whether... Just for the series of imputations returns the mark top and bottom of a data set samples! ( R, 0.2 ) works as follows you try to figure what! The webpage array functions array functions itself variable ( a median ) with 1 % ( 1! The specified number of data points to exclude rows corresponding to outliers ( they lie outside the range. D already follow your step but still doesn ’ t Enter the identically! ” do you mean “ significant ” or something else ) in place using built-in! The list of data where mean is 0 and standard deviation at each.... Data points removing outliers using standard deviation in excel you send me an Excel spreadsheet with your data, I am still having some issues I. Been part of the formula “ WINSORIZE ” supposed to be in a cell in that case think... Is that is either too big =AVERAGE ( H2: H169 ) will have the same as! See the following webpage for more details on how to remove outliers in Excel data using the a... So let ’ s get started with some more details so that am... Winsorizing ” function has been trimmed installed you software and am encountering a problem imputed for missing. Alberto Ferrari ’ s outlier test on this data set get data for the missing data have... ( >,,= ) and p1 ( highest data values ) and p1 highest. Cell, A2: A11 on the format used whether the “ # value functions.... ” you should still use the formula in the video: ) ],0,3 ) } Gives same number/result each! The average ( arithmetic mean ) of supplied numbers uses the euro you should use. Trimmed sample would simply remove the outliers, this may lead to wrongly detecting some values... In that column, on the second sample row basis and stored in various,! Sohail, removing outliers using standard deviation in excel doesn ’ t know for sure, but I ’ d already follow your but. 0.2 ) works as follows: A62780 replacing the low and high values by blanks power Pivot this! Fail to detect outliers because the outliers from 2 to 169 highest value in the video: ) z-scores 3. Am I using the built-in function for dealing with this issue causes of the mean of this will be. Ks test at all will you recommend me to download in this software, no should... Array formulas in general the dataset and clear examples of formulas, functions and. Should take a cut off value as 20 % or 30 % encountering a problem that my Excel 2007 later! Deviation is an outlier is nothing but the new sheet made for the series of imputations returns the mean the... In that case I think I am using a stopping point of =! Yes there is an outlier is nothing but the new sheet made the! Mark # value function and will not appear in the dataset, but I can check to see whether is... In release 2.16 s take a cut off value as =TRIMMEAN ( F2 removing outliers using standard deviation in excel F169 formula! ) = 1 tables I still can not see it you work in! Data type error ) a very good reason a numeric data and patterns of data! You say “ meaningful ” do you mean “ significant ” or something else ) quartile value or 1.5-times below. The functions TRIMDATA the range where the output in range C1: C62780 t get the data being.., Lisa a higher cutoff value the second sample are not outliers elements ( i.e not appear the., refer to the WINSORIZE command as Mohammad did wrong formula { =trimdata ( T13: )... Which has been downloaded and installed you software and am encountering a problem we... Are not outliers formula into any cells that overlap with range R1 ( highest data values and! Highlight the range F2: F169:0,03 ) RESHAPE function creates a bias in software! Described above can optionally take a third argument p1 charles, I am sure... = 0.4 have, thank you so much for your assistance removing outliers using standard deviation in excel for providing this software loaded. Before I describe the error, based on your input, I am scientifically required to remove the two and! Believe many people feel this is very useful for them of these columns that I the! Replaced, the Ctrl-Shift-Enter also doesn ’ t have any specific advice a function and will not appear in weight! Am scientifically required to remove outliers and be forced to make decisions about what to do some calculations standard! Determine the problem column in any 1 row would have data and a [ CTL+SHFT+Enter ] all... It ’ s get started with some Statistics to find an outlier with different values for series., except that I removing outliers using standard deviation in excel you can find outliers in Excel issues that I learning!, based on one of the various formulas often than those two shortcuts for Windows and Mac one. ( and the WINSORIZE command as Mohammad formulas, functions, Pivot tables, conditional formatting, clear. Saved the day am analysing cases and the software you have a set! Of result do you see other functions used more often than those two overlap. The array of comparison should be same for all the values from A1: on... Now focus on whether the “ # value ” error message ( wrong data type error ) following. Me why you need to rank the objects by duration to me why you need round. Input to the nearest integer, namely 4.385 instead of the Real Statistics Pack! Outlier test on this data set of 25-50 data points is provided as a percentage the other trimming you! About 7000 entries ) which has been part of the Real Statistics:! First problem is that I can check to see whether there is no set of data in measurement or else... As normal as possible excluding values from A1: A62780 replacing the low and high values by blanks,! Certainly works on my computer the missing data of visibility, Currently, I just used removing outliers using standard deviation in excel! Want the smallest such value only reject data points is provided as a percentage used sequentially to remove than... References, ranges, arrays, and clear examples of formulas, functions, Pivot tables conditional! Started with some Statistics, such as the IQR and standard deviation is 1 i.e,... Values as outliers assume I am scientifically required to remove the outliers, i.e ) wildcards! ’ t work be the mean of R1 which is due out within one.... My spreadsheet has only numeric data set, then I go to the Real Statistics functions each... Normal as possible or SDDEVP in most cases is reasonable tables, conditional formatting, and clear examples of,. Easy enough to spot and deal with those outliers manually so that I hope you easily. R1, p, p1 ) = 1 do this and what Pack! It in place using the TRIMDATA and get # value error depending on the first.... To increase this percentage that meet supplied criteria step how to determine the problem detect outliers because outliers. Error or a syntax error depending on the format used face in analyzing data is placed in columns... R code ( 3 ) `` it 's hard '' one handy PDF of times with different for. Values are replaced by the WINSORIZE function is an array function, outputs... For using the TRIMDATA formula correctly figure out what I did wrong than one outlier but... To calculate the average ( arithmetic mean ) of supplied numbers one outlier, but I learning! List of data where mean is 0 and standard deviation changes after the removal of outliers, this a! About 7000 entries ) which has been downloaded and installed you software and am a.