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The weighted mean is a type of average that takes into account the relative importance or frequency of each value in a dataset. Unlike a simple mean, where all values contribute equally, the weighted mean assigns different weights to each value based on their significance. This is particularly useful in scenarios where certain data points are more relevant, such as calculating averages over varying time periods or quantities.

Data representation involves organizing and summarizing data in a way that makes it easier to analyze and interpret. In the context of the credit card balance example, the data is represented by different balances over specific days. Understanding how to represent this data accurately is crucial for calculating the weighted mean, as it allows for clear identification of the values and their corresponding weights.

To calculate the weighted mean, you multiply each value by its corresponding weight, sum these products, and then divide by the total of the weights. In the credit card balance example, each balance is multiplied by the number of days it was held, and the total of these products is divided by the total number of days in October. This process ensures that the average reflects the influence of each balance based on the time it was maintained.