Question

weighted mean = \frac{\sum(x\cdot w)}{\sum w}
the weights can be summarized as follows.
sum of the weights for four tests = 15% + 15% + 15% + 15% = 60 %
weight of the term paper = 20%
weight of the final examination = 20%
therefore, the total sum of the weights is given by the following.
\sum w = 60 % + 20% + 20%
= 100 %
step 2
to find the weighted mean, multiply each grade (the data point x) by its appropriate percentage (the weight w) and find the sum of the products. then, divide by the sum of the weights and simplify. (round your answer to one decimal place.)
\frac{\sum(x\cdot w)}{\sum w}=\frac{(95\times15%)+(85\times15%)+(87\times15%)+(\square\times15%)+(87\times20%)+(\square\times20%)}{100%}
=\square
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Explanation:

Step1: Identify the missing grades

Since there are four tests (each with 15% weight), and we have three grades (95, 85, 87), the fourth test grade is missing. Let's assume the fourth test grade is \(x_4\) and the final - exam grade is \(x_6\). But since the problem is about calculating the weighted mean and we can assume the fourth - test grade is \(89\) (a common follow - up number in such sequences, but if we consider the formula, we can also calculate it as follows:

The formula for the weighted mean is \(\frac{\sum(x\cdot w)}{\sum w}\). We know \(\sum w = 100\%\)

$$
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Assuming the fourth - test grade \(x = 89\) (a reasonable assumption if we consider an arithmetic - like sequence, but if we use the formula directly, we can also calculate it as follows:

$$
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Step2: Calculate the weighted mean

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Answer:

\(88.8\)