what is the purpose of a weighted average 
in calculating a simple average or arithmetic mean all numbers are treated equally and assigned equal weight but a weighted average assigns weights that determine in advance the relative importance of each data point in calculating a weighted average each number in the data set is multiplied by a predetermined weight before the final calculation is made a weighted average is most often computed to equalize the frequency of the values in a data set for example a survey may gather enough responses from every age group to be considered statistically valid but the 18 to 34 age group may have fewer respondents than all others relative to their share of the population the survey team may weigh the results of the 18 to 34 age group so that their views are represented proportionately however values in a data set may be weighted for other reasons than the frequency of occurrence for example if students in a dance class are graded on skill attendance and manners the grade for skill may be given greater weight than the other factors each data point value in a weighted average is multiplied by the assigned weight which is then summed and divided by the number of data points the final average number reflects the relative importance of each observation and is thus more descriptive than a simple average it also has the effect of smoothing out the data and enhancing its accuracy weighting a stock portfolioinvestors usually build a position in a stock over a period of several years that makes it tough to keep track of the cost basis on those shares and their relative changes in value the investor can calculate a weighted average of the share price paid for the shares to do so multiply the number of shares acquired at each price by that price add those values then divide the total value by the total number of shares a weighted average is arrived at by determining in advance the relative importance of each data point for example say an investor acquires 100 shares of a company in year one at 10 and 50 shares of the same stock in year two at 40 to get a weighted average of the price paid the investor multiplies 100 shares by 10 for year one and 50 shares by 40 for year two then adds the results to get a total of 3 000 then the total amount paid for the shares 3 000 in this case is divided by the number of shares acquired over both years 150 to get the weighted average price paid of 20 this average is now weighted with respect to the number of shares acquired at each price not just the absolute price the weighted average is sometimes also called the weighted mean advantages and disadvantages of weighted averageweighted average provides a more accurate representation of data when different values within a dataset hold varying degrees of importance by assigning weights to each value based on their significance weighted averages ensure that more weight is given to data points that have a greater impact on the overall result this allows for a more nuanced analysis and decision making process next weighted averages are particularly useful for handling skewed distributions or outliers within a dataset instead of being overly influenced by extreme values weighted averages take into account the relative importance of each data point this means you can manipulate your data set so it s more relevant especially when you don t want to consider extreme values thirdly weighted averages offer flexibility in their application across various fields and disciplines whether in finance statistics engineering or manufacturing weighted averages can be customized to suit specific needs and objectives for instance like we discussed above weighted averages are commonly used to calculate portfolio returns where the weights represent the allocation of assets weighted averages can also be used in the manufacturing process to determine the right combination of goods to use one downside of a weighted average is the potential for subjectivity in determining the weights assigned to each data point deciding on the appropriate weights can be challenging and it often involves subjective judgment where you don t actually know the weight to attribute this subjectivity can introduce bias into the analysis and undermine the reliability of the weighted average weighted averages may be sensitive to changes in the underlying data or weighting scheme small variations in the weights or input values can lead to significant fluctuations in the calculated average making the results less stable and harder to interpret this sensitivity can be particularly problematic in scenarios where the weights are based on uncertain or volatile factors which may include human emotion i e are you confident you ll feel the same about the appropriate weights over time last the interpretation of weighted averages can be more complex compared to simple arithmetic means though weighted averages provide a single summary statistic they may make it tough to understand the full scope of the relationship across data points therefore it s essential to carefully assess how the weights are assigned and the values are clearly communicated to those who interpret the results accurate representation via weighted significance aiding nuanced decision making 