Search Results for: weighted mean

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 … Read More

Introduction For any set of weights W = {w1, w2, …, wn} where each wi ≥ 0 and wi > 0 for at least one i, the weighted mean of a sample S = {x1, x2, …, xn} is defined by where The biased weighted variance of the sample is When all the weights are the same, this reduces to the usual which is … Read More

Weighted norm The weighted norm for a vector X = (x1, x2, …, xn) and weights W = (w1, w2, …, wn), where each wi ≥ 0 and wi > 0 for at least one i, is defined by where w = the sum of the wi. Weighted distance The weighted Minkowski distance between vectors … Read More

Basic Concepts In Example 1 of Simple Moving Average Forecast, the weights given to the previous three values were all equal. We now consider the case where these weights can be different. This type of forecasting is called weighted moving average. Here we assign m weights w1, …, wm, where w1 + …. + wm … Read More

Data Analysis Tool Real Statistics Data Analysis Tool: The Real Statistics Resource Pack provides the K-Means Cluster Analysis data analysis tool which automates the steps described in K-means Cluster Analysis. We show how to use this tool via the following example. Example 1: Perform cluster analysis to classify the data in range B3:E18 of Figure … Read More

Basic Concepts Cohen’s kappa takes into account disagreement between the two raters, but not the degree of disagreement. This is especially relevant when the ratings are ordered (as they are in Example 2 of Cohen’s Kappa). To address this issue, there is a modification to Cohen’s kappa called weighted Cohen’s kappa. Weighted kappa is calculated using … Read More

As described in Frequency Tables, you can’t simply use the Excel functions AVERAGE and VAR.S to calculate the mean and variance for data in the form of a frequency table. One approach to addressing this issue is to use a function that converts data in the form of a frequency table to raw data, from … Read More

Basic Concepts In an unbalanced ANOVA, the sample sizes for the various cells are unequal. Provided the cell sizes are not too different, this is not a big problem for one-way ANOVA, but for factorial ANOVA, the approaches described in Factorial ANOVA are generally not adequate. In these cases, the regression approach described in ANOVA … Read More