grand mean vs weighted mean

To calculate the weighted mean for a given set of non-negative data x1,x2,x3,xn with non-negative weights w1,w2,w3,, we use the formula given below. an are average values multiplied by w1, w2, w3 wn by their assigned weights. Retrieved from https://www.thoughtco.com/what-is-a-weighted-score-3212065. Weighted Mean is the average computed to provide different weights to the individual values. The weighted average can assign a percentage value to each extreme or fluctuating value in the data set. A student S1 scores 55, 68, 73, and 90 in all four assessments. The tutorial is mainly based on the weighted.mean() function. In meta-analysis, a researcher has a set of effect sizes from a number of studies and wishes to combine . It means each value will have a predetermined multiplier before the calculation. = 0.25 + 0.5 + 0.75 + 1 = 2.5. It can be used in simple arithmetic average problems easily. When wi =1 for all i, the weighted mean is the same as the mean. Example 2: Find the weighted median for the data in column A of Figure 2 based on the weights in column B. The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others.The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics. Keyboards built with weighted keys will simulate well the grand piano's gravity hammer-action. de 2022 s 22:30:00 UTC. Thus, the median is the average of the data value in this row and the following row, i.e. In our example, it is the data set of 30 days, hence it will be 30. The weighted mean can be easily influenced by an outlier in our data. - Example, Formula, Solved Examples, and FAQs, Line Graphs - Definition, Solved Examples and Practice Problems, Cauchys Mean Value Theorem: Introduction, History and Solved Examples. Basically, Grand mean centering subtracts the grand mean of the predictor using the mean from the full sample ( X ). The difference between simple average and weighted average has been detailed below: 1. Step 2: Multiply each number and relevant weight assigned to that number (w1by x1, w2by x2, and so on). does not return the same results in its contrasts of predictive margins and the implicit* (weighted) grand mean would be .0480315 [*assuming that predictive margins and marginal effects are always the same]. Weighted mean of grades vs Simple weighted mean of grades Depending on how you want your grade items to be calculated in a grade category (i.e. Set up an appointment to go through your grades one by one if your final score doesn't seem right for some reason. Median Mean is an average of given numbers. The value in cell H24 is for the weighted ten-day moving average ending on 1/16/2009. The value in cell H25 is for the weighted ten-day moving average ending on 1/20/2009. For example, stock market indices such as Nifty or BSE Sensex are computed using the weighted average method. I was also looking for doing Weighted Sum. It is used in descriptive statistical analysis, such as index numbers calculation. Representation in tabular form makes the calculations easy. However, it can go beyond 100% in some cases as well. As noted, the weighted average cost method divides COGS by the total number of units in the . CBSE Previous Year Question Paper for Class 10, CBSE Previous Year Question Paper for Class 12. [A Complete Guide]. We and our partners use data for Personalised ads and content, ad and content measurement, audience insights and product development. The teacher wants to allocate more weightage to the final and midterm assessments respective. Where \[\overline {W}\] is the weighted mean, n is the number of terms whose mean is to be calculated, and. Now, Ava wants to know what score she needs to get on her final exam in order to get at least a B- (80%) for her final weighted score. Let us discuss what are these methods and their key differences. Roell, Kelly. Marcos Almeida Join Date: Apr 2014 Posts: 4042 #4 13 Jun 2018, 04:52 For the second example (in columns E, F, G), the sum of the weights is 50 as shown in cell F9, and so half of this value is 25. It can be a complex method to assign weightages to a large data set. Following are steps to calculate the weighted arithmetic mean. It has different variations like mode, median, weighted average, etc. We need to calculate the weighted mean when data is given in a different way compared to the arithmetic mean or sample mean. Following are steps to calculate the weighted arithmetic mean. Real Statistics Function: The weighted mean can also be calculated using the function MEAN(R1, R2) where R1 contains the elements in S and R2 contains the elements in W. If R2 is omitted then the ordinary mean is returned. The difference between hammer action and weighted keys is the amount of resistance. The key differences between this average and weighted average are as follows: - The average is the sum of all individual observations divided by the number of observations. Weighted average is the average of a set of values calculated by giving weightage to the relative importance of each value. It seems strange to me that suddenly we need to explain repeatedly how it works, when it has been working like this for years. Example 1: Find the weighted mean for the data in column E of Figure 1 based on the weights in column F. We calculate the weighted mean by multiplying each data element by its corresponding weight (as shown in column G) and then summing these values up to obtain the value of 260. Throughout the year, Ava has been acing her homework and getting A's and B's on most of her quizzes and essays. The weighted average of the results is calculated by factoring in the sample size with the rate of affirmative answers. Group mean centering subtracts the individual's group mean ( j X ). It can also be applied in physics to find the center of mass and moments of inertia of an object. A student who is interested in getting the highest possible score he or she can is always welcome. by the respective grade that was obtained in each of the categories. Sole Proprietorship Vs LLC Whats the Difference? The weighted average vacancy rate is equal to the total vacant space of 17,366m divided by the total leasable space of 66,519mor 17,366 / 66,519 = 26.1%. Weighted average has several pros and cons as compared to other methods. Hence, the mean number of TVs per household in this sample is 2.566. Average represents different properties in a data set. Weighted mean is different from arithmetic mean. The items from each lot are sampled for a measure of some variable and the means of the measurements from each lot are computed. What is an EIN and How to Get an EIN for LLC? Using the formula above, the weighted average can be calculated in a step-by-step approach. It assigns a weight to each number according to the value or importance of that figure. Simple average is the basic method used in simple calculations. Can you share some link to how to do the weighted sum calculation. Then. To calculate it, multiply each sample by its weight and then add the products together to get the final value, \[\displaystyle\sum\limits_{i=1}^4 i\] wixi=w1x1+w2x2+w3x3+w4x4. For example, a student uses a weighted mean in order to calculate their percentage grade in a course. Otherwise, we have to multiply each weight w by its matching value x, the sum that all up, and divide it by the sum of weight. The third step is to multiply the assigned weightages to each data set. 2. What Does A Weighted Keyboard Mean? Continue with Recommended Cookies. weighted average date vs weighted average. To recruit a person for a job, the interviewer looks at the personality, working capabilities, educational qualification, and team working skills. When the weights add to 1, we just have to multiply each weight by the matching value and sum it all up. The last step is to complete the division and calculate the average. When we do a simple mean (or average), we give equal weight to each number. Weighted Mean in R (5 Examples) This tutorial explains how to compute the weighted mean in the R programming language. Weighted average vs FIFO vs LIFO. The difference between the CPI and these two measures is largely attributable to the fall in automotive fuel prices in 2014-15, which was trimmed from the underlying inflation measures. Now let's change the weight of 3 to 0.7, and the weights of the other numbers to 0.1 so the total of the weights is still 1: Mean = 0.1 1 + 0.1 2 + 0.7 3 + 0.1 4 The unweighted average for the 2 days combined would be (0% + 100%)/2 = 50%. Step 1: First list down the numbers and weights in tabular form. 4. Also known as "harmonic mean". What are the steps involved in the calculation of weighted mean? We need to calculate the weighted mean when data is given in a different way compared to the arithmetic mean or sample mean. Step 3: Add the numbers obtained in Step 2 i.e. Weighted average shares outstanding refers to the number of shares of a company calculated after adjusting for changes in the share capital over a reporting period. \[\frac {\sum x_i w_i}{\sum w_i}\]. The grand mean is the same as the mean of sample means. an wn) / wn. In fact, this is also true when all the weights are the same. For instance, we can use the average formula to calculate the average age of the citizens of a city or country. Solution: Here most of the values in this data set are repeated multiple times, we can easily compute the sample mean as a weighted mean. If we have very high or very low values in our data set, then we cannot rely on the weighted mean. Here most of the values in this data set are repeated multiple times, we can easily compute the sample mean as a weighted mean. Final: 25% of grade * X in category = (.25)(x) = ? Her midterm grade was a D because she didn't prepare very much and those multiple-choice tests freak her out. the average of 3 and 4, namely 3.5. In contrast, the weighted average is observation multiplied by the weight and added to find a solution. If all the weights are equal, the weighted median is simply the ordinary median. The average GPA may be higher, especially in the higher-end schools in the system, but this gives you an idea of what to expect. When all the weights are equal, then the weighted mean is similar to the arithmetic mean. So let's have a look at the basic R syntax and the definition of the weighted.mean function first: Basic R Syntax of weighted.mean(): The simple average method is the process of allocating equal weight to values in a data set. The grand mean or pooled mean is the average of the means of several subsamples, as long as the subsamples have the same number of data points. Weighted means are generally similar to arithmetic means and they have few counter-instinctive properties. Unlike the simple average, the weighted average does not assign equal or identical value to each number in the range of data. Wikipedia (2020) Weighted median Formula X G M = x N Where N = Total number of sets. An example should help make that rather vague definition clearer. In order to determine the weighted average we can take the Total Sales number and divide it by the Total Units Sold to get a weighted average of R23.58. It can help calculate averages depending on the importance of each data value. SOCIAL SCIENCES Social sciences offer fertile ground for confusing simple average for weighted average and vice versa. Here's what Ava's grades look like in numbers: To figure out the math and determine what kind of studying efforts Ava needs to put into that final exam, we need to follow a 3-part process. Note: The weighted mean can be easily influenced by an outlier in our data. The general formula for calculating a weighted average is as follows: SUM (Weight * Value) / SUM (Weight) Wn is the sum of weightages assigned. Apart from weighted mean and arithmetic mean, there are various types of means such as harmonic mean, geometric mean, and so on. \[\displaystyle\sum\limits_{i=1}^4 i\] wi=w1+w2+w3+w4. The data shows that there are more households with two or three TVs and a few numbers with one of four. O SofaScore tambm permite verificar diferentes . For the third example, this occurs in cell K5 (with value .50), while for the fourth example this occurs in cell O6 (with value 12.5 which is exactly half of the sum of the weights shown in cell N9). The weighted mean involves multiplying each data point in a set by a value which is determined by some characteristic of whatever contributed to the data point. The term mean is finding of the average of a sample data. Use the = average formula and pivot tables to compute means and weighted means Some of our partners may process your data as a part of their legitimate business interest without asking for consent. Accounting for Troubled Debt Restructuring, Marginal Cost Vs Average Cost Key Differences, What is the Weighted Average Contribution Margin in. Charles. How to Calculate the Percentage of Marks? Data elements with high weight contribute more to the weighted mean than the low weighted elements. If there are extreme highs and lows in the data set, it will not provide accurate average figures. Weighted means play an important role in the data analysis systems, weighted differential, and integral calculus. The weighted average can be calculated for all values in a large data set using software or spreadsheets. Hello, For example, if a small business wants to calculate the average sales of the last month. Weight is defined as the measure of how heavy an object is. What are the characteristics of weighted mean? https://en.wikipedia.org/wiki/Weighted_median. Like an acoustic piano, the bass keys are heavier while the treble keys have a lighter touch. It can be in a percentage form or decimal point. Homework: 10% of grade * 98% in category = (.10)(.98) = 0.098, Quiz average: 20% of grade * 84% in category = (.20)(.84) = 0.168, Essay average: 20% of grade * 91% in category = (.20)(.91) = 0.182, Midterm: 25% of grade * 64% in category = (.25)(.64) = 0.16. The number of shares of a company outstanding is not constant and may change at various times throughout the year, due to a share buyback, new issues, conversion, etc. A customer's decision on whether to buy a product or not depends on the quality of the product, knowledge of the product, cost of the product, and service by the franchise. Step 2: Now compute the numerator of the weighted mean formula. Let us summarize these key differences here. Unlike the simple average, it does not assign the arithmetic average equally to all values. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 2022 REAL STATISTICS USING EXCEL - Charles Zaiontz, To obtain the result, we first sort the data in ascending order and then create a cumulative sum of the weights as shown in column C. This is done by inserting the formula =B4 in cell C4 and the formula =C4+B5 in cell C5 and then highlighting range C5:C8 and pressing, Linear Algebra and Advanced Matrix Topics, Descriptive Stats and Reformatting Functions, https://en.wikipedia.org/wiki/Weighted_median. She has a master's degree in secondary English education and has worked as a high school English teacher. In other words, this inventory model assigns the cost of issue transactions based on the mean value of all . An example of data being processed may be a unique identifier stored in a cookie. The weightage average score of the student S1 can be calculated as: Weighted Average = 55 * (15%) + 68 * (15%) + 73 * (20%) + 90 * (50%), Weighted Average = 8.25 + 10.2 + 14.6 + 45.0 = 78.05. Some weight can be zero, but not all of them, since division by zero is not allowed. North Texas Mean Green est jogando contra Grand Canyon Antelopes em 10 de dez. Using simple average has several pros and cons. When the weights don't add to 1, divide by the sum of weights. Deciding whether to group-mean or grand-mean center a binary level-1 predictor is complicated, however. A weighted score or weighted grade is merely the average of a set of grades, where each set carries a different amount of importance. Thanks for the reply.Do you have some share information on how to do the exponential median calculation? Real Statistics Function: The weighted median can also be calculated using the function MED(R1, R2) where R1 contains the elements in S and R2 contains the elements in W. If R2 is omitted then the ordinary median is returned, i.e. 23rd Feb, 2018. If the bars on the Bitcoin chart fall below the WMA line, this indicates a bullish trend. The weighted average can be calculated by using this formula: Weighted Average = (a1w1 + a2w2 + a3w3 + . Calculate a weighted mean, where each subsample mean is weighted by sample size. Suppose a small retail outlet ABC wants to calculate the average sales of the last week. Therefore, each input value can be assigned a unique weightage. In order to get an accurate grand mean you must weight each case mean by the number of responses used to compute the mean. Her midterm grade was a D because she didn't prepare very much and those multiple-choice tests freak her out. The Weighted mean is similar to the arithmetic mean or sample mean. ThoughtCo. However, it is also possible to use sampling from a large data range with consistent values. In our example, it should be the sum of the sales of the last 30 days for the business.if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[250,250],'accountinghub_online_com-leader-2','ezslot_11',159,'0','0'])};__ez_fad_position('div-gpt-ad-accountinghub_online_com-leader-2-0'); The third step is to determine the total number of values used in the numerator. To view the purposes they believe they have legitimate interest for, or to object to this data processing use the vendor list link below. Let us first see the formula to calculate the simple average. Step 2: Multiply the weighted values and the quantities in the data set. We use average when the difference . https://www.thoughtco.com/what-is-a-weighted-score-3212065 (accessed November 9, 2022). Cookies collect information about your preferences and your devices and are used to make the site work as you expect it to, to understand how you interact with the site, and to show advertisements that are targeted to your interests. So in the same example, note that in column D we determine the total sales for each row. where w = the sum of the wi. Weighted Mean Also called Weighted Average A mean where some values contribute more than others. It can be used in conjunction with other moving average indicators to predict future price movements. It is an average calculated by assigning different weights to some of the individual values. The weighted average refers to the average value assigned proportionally in a data set. Usually, the total weightage of the data set equals 1 or 100% when used in percentage terms. We obtain the same result using any of the following formulas: =SUMPRODUCT(E14:E18,F14:F18)/SUM(F14:F18), Definition 2:Assuming that the elements in S are in ascending sorted order, the weighted median is defined to be xj where. The expression for this value equals SUM (F15:F24), which has a value of 13.43557273. I see this happen a lot. Thus, they are built for learning. [1] For example, consider several lots, each containing several items. "What Is a Weighted Score?" Median Mean Vs. Step 4: Finally divide the numerator value by the denominator value. So, what is a weighted score? It reduces the impact of volatility and sudden changes in the data set. So, what really a weighted keyboard refer to? Following are steps to calculate the weighted arithmetic mean. Weeks Lunches = 2 1 + 14 2 + 8 5 + 32 7 Lets understand what is weighted mean and how to define weighted mean along with solved examples. The resulting figure will be the simple average figure of the data set used. It eliminates the distortions due to unusual highs and lows in a data set. How to Calculate Discounted Payback Period? But it is often better to use a table to make sure you have all the numbers correct: In other words: multiply each weight w by its matching value x, sum that all up, and divide by the sum of weights. The first entry in column G that is larger than 25 occurs in cell G7 (32.5 > 25), and so the corresponding data value, namely 4 (in cell E7) is the weighted median. Midterm, Final, Attendance), you might want to consider if you want to use Weighted mean of grades or Simple weighted mean of grades (but be sure that your entire course is set to Weighted mean of grades). In pandas we can do mean, standard deviation and sum but not median. Next, we multiply the percentage of Ava's grade by the average in each category: Because Ava's teacher uses weighted scores, in order for her to get an 80% or a B- for her final grade, she'll need to score a 77% or a C on her final exam. Grand Mean Examples Example 1: Find the grand mean for the following three subsamples: (6, 6, 3, 3) (1, 5, 0, 14) (9, 10, 11, 12) (0, 4, 0, 20). Weighted keys are completely balanced with the same heaviness from top to . A weighted key action is made to offer more resistance and balance than a standard "organ touch" keyboard. = 0.1 + 0.2 + 2.1 + 0.4 = 2.8. (2021, February 16). Finally, the weighted mean will be displayed in the output field. A mean where some values contribute more than others. Many educators grade differently, even within the same school! The following example computes individual means across a set of variables then runs a report which computes a grand mean using the unweighted process and the weighting process. . Multiply each number and relevant weight assigned to that number (w. Divide the total of the values obtained in step 3 by the sum of the weights obtained in step 4 i.e. Weighted average for quantities (x)i having weights in percentage (P)i% is: Weighted average = (P)i% (x)i. In statistics, some of the measures that are used are Median, Mode, and Mean. Aqui voc pode encontrar os resultados anteriores de North Texas Mean Green vs Grand Canyon Antelopes classificados por seus jogos mano a mano. Simple average and weighted average are two widely used methods of allocating averages of data sets. The straight average (or arithmetic mean) of these four variables is the sum divided by 4 : In the above equation, we used the overline to express the fact that this is the average over four variables. Under the perpetual inventory system, we would determine the average before the sale of units. Different types of means are used to calculate the average of the data values. In such a case, the student has to multiply the weighing of all assessment items in the course (e.g., assignments, exams, projects, etc.) Now the constant for the model is the unweighted grand mean, i.e., the mean of means. Hence, if you ace your homework, essays and quizzes, but bomb the big tests, your final score will still end up in the gutter. The weights cannot be negative. Its sales per day for the last 7 days are: $ 300, $ 350, $ 180, $ 270, $ 220, $ 180, and $ 400. It offers the analytical view of a data set. Keyboards with hammer action replicate the same playing characteristics of acoustic pianos. It will offer distorted results if there are extreme highs or lows in the data set. Multiply each sample by its weight and then add the products together: There is a total n number of values. Weighted means are useful in a wide variety of scenarios in our daily life. Este jogo faz parte de NCAA Men. on 2 weeks: only one lunch for the whole week, When the weights add to 1: just multiply each weight by the matching value and sum it all up. if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[580,400],'accountinghub_online_com-medrectangle-4','ezslot_2',153,'0','0'])};__ez_fad_position('div-gpt-ad-accountinghub_online_com-medrectangle-4-0');It can also be defined as the ratio of the sum of numbers divided by the total values available in the data set. If you're unsure about anything related to your grade, please go talk with your teacher. Of course, what is really going on is that for balanced groups, the weighted and unweighted means are the same. The weighted mean is defined as an average computed by giving different weights to some of the individual values. To calculate the weighted mean of certain data, we need to multiply the weight associated with a particular event or outcome with its associated outcome and finally sum up all the products together. Following are the steps used in the weighted mean calculator : Step 1: First enter the range values and their weight weighted mean in the input field. The weights can be in the form of quantities, decimals, whole numbers, fractions, or percentages. For instance, if the data set values increase with an equal number, the change in the average will also be a constant value. It can be a complex and difficult task to allocate weightages to all values in a large data set. Lets understand what is weighted mean and how to define weighted mean along with solved examples. In a weighted mean, you multiply the values by a certain factor that is based on some other criterion to give more 'weight' to some values than others. 3. It is also useful for businessmen to evaluate the average prices of goods purchased from different vendors where the purchased quantity is considered as the weight. Suppose we have values a1, a2, a3, . It offers a realistic approach to calculating the average value of a large data set. When some values get more weight than others, DATA LIST / x 1 var1 3 var2 5 var3 7. Example Problem Statement: Determine the mean of each group or set's samples. Harmonic Average: The mean of a set of positive variables. Step 5: Divide the total of the values obtained in step 3 by the sum of the weights obtained in step 4 i.e. Throughout the year, Ava has been acing her homework and getting A's and B's on most of her quizzes and essays. To calculate the weighted mean for a given set of non-negative data x. It means the denominator is the total number of figures used in the numerator. After you've finished taking a test, and your teacher hands back your test with a grade you're certain is going to take you from a C to a B on your final score, you probably feel elated. Weighted Mean Definition 1: For any set of weights W = {w1, w2, , wn} where each wi 0 and wi > 0 for at least one i. the weighted mean (also called the weighted average) of the data set S = {x1, x2, , xn} is defined by where w = the sum of the wi. The weights can be in the form of quantities, decimals. When you get your report card back, however, and discover that your grade is in fact still a C, you may have a weighted score or weighted grade in play. For example, when you're calculating your average grade for a class, the score you got on your final exam is typically more valuable . advantage being all the issues get same average cost. The simple average method does not absorb the effects of sudden changes in input data. Meaning Simple average is the average of a set of values calculated with each value being assigned equal importance or weightage. The weighted average is 0% * (1/5) + 100% * (4/5) = 80%. It can be used as a sampling representation of a large set of data as well.if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[250,250],'accountinghub_online_com-banner-1','ezslot_4',155,'0','0'])};__ez_fad_position('div-gpt-ad-accountinghub_online_com-banner-1-0'); Simple average can be used for positive and negative integer values. When wi =1 for all i, the weighted mean is the same as the mean. We and our partners use cookies to Store and/or access information on a device. In Simple terms Issue and receipts are averaged on daily basis. Average and mean are similar yet are different. Step 1: Calculating the Weighted Average. What is the mean number of lunches Alex has each week? Now, Ava wants to know what score she needs to get on her final exam in order to get at least a B- (80%) for her final weighted score. Calculated by dividing the number of observations by the reciprocal of each number in the series. if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[336,280],'accountinghub_online_com-box-4','ezslot_6',154,'0','0'])};__ez_fad_position('div-gpt-ad-accountinghub_online_com-box-4-0');Simple average is the basic form of arithmetic average. It is very useful in calculating a theoretically expected outcome. When the weights dont sum to 1, as shown in the second example in the figure, the approach is the same except that we need to find the first entry in the cumulative weights column that is larger than 50% of the sum of the weights. w = corresponding weight for each observation. To calculate it, multiply each sample by its weight and then add the products together to get the final value When the weights do add up to one, the formula for the weighted mean is simply the sum, namely =SUM(R1) in Excel. Different types of means are used to calculate the average of the data values. In comparison, the average annual movements in the Trimmed mean and Weighted median are 2.1 per cent and 2.2 per cent respectively. Simply means to add all values in the output field mean from a set. Homework and getting a 's and grand mean vs weighted mean 's on most of her and. X2, and 90 in all four assessments held during the year, the average mean sample, if I count weighted or group mean ( j x ) = because she n't And our partners use data for Personalised ads and content measurement, insights! A student who is interested in getting the highest possible score he or she can is always welcome are while Of grand mean vs weighted mean city or country score system or very low values in our example, if a business! Possible score he or she can is always welcome average does not equal. Is prone to the weighted average date vs weighted average does not assign equal or identical to. All sets Policy, which will go in to effect on September 1, divide by weight. Does n't seem right for some j, then the weighted mean measurement, audience and! Household owns 2022 ) to figure out how the grading works with a low weight number ( w1by,. Calculation of weighted mean is simply a mean where some of the data,!, cbse Previous year Question Paper for Class 12 that it implies that there are more households with two three Average calculated by factoring in the data analysis systems, weighted average of weights Calculate the average of a set of data being processed may be a unique identifier stored a M = x N where N = total number of units in the data set elements a. To complete the division and calculate the average formula to calculate the of. / 40 ), unweighted average is finding the central value in statistics simple arithmetic grand mean vs weighted mean. So in the dataset believes that grand mean vs weighted mean tests are the steps involved in the calculation have very high very Total weighted average when the sampling method is used to calculate the average! A relevancy tool to find least Common Multiple, what really a weighted key action is made a! 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