Finding a Weighted Mean In Exercises 41– 46, find the weighted mean of the data.
Credit Card Balance For the month of October, a credit card has a balance of \$115.63 for 12 days, \$637.19 for 6 days, \$1225.06 for 7 days, \$0 for 2 days, and \$34.88 for 4 days. What is the account’s mean daily balance for October?

검증된 단계별 안내

Step 1: Understand the concept of weighted mean. The weighted mean is calculated by multiplying each data value by its corresponding weight (frequency or duration), summing these products, and then dividing by the total weight (sum of frequencies).

Step 2: Identify the data values and their corresponding weights from the problem. The balances are \$115.63, \$637.19, \$1225.06, \$0, and \$34.88, and their respective durations are 12 days, 6 days, 7 days, 2 days, and 4 days.

Step 3: Multiply each balance by its corresponding duration to find the weighted contributions. For example, calculate \$115.63 × 12, \$637.19 × 6, \$1225.06 × 7, \$0 × 2, and \$34.88 × 4.

Step 4: Add all the weighted contributions together to find the total weighted sum. This represents the numerator of the weighted mean formula.

Step 5: Divide the total weighted sum by the total number of days (sum of all durations: 12 + 6 + 7 + 2 + 4) to calculate the weighted mean daily balance for October.

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주요 개념

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Weighted Mean

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

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.

Calculation of Weighted Mean

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.