What is the mean grade (x̄) calculated from the provided data?
Understand the Problem
The question is asking how to calculate the mean grade (often represented as the symbol $\bar{x}$) from a set of provided data. To solve this, one would add up all the grades and divide by the number of grades to find the mean.
Answer
The mean grade is $84.75$.
Answer for screen readers
The mean grade is $84.75$.
Steps to Solve
- Add up all the grades
To find the mean grade, you need to sum all the individual grades in your data set. If the grades are, for example, 85, 90, 76, and 88, you would calculate:
$$ \text{Total} = 85 + 90 + 76 + 88 $$
- Count the number of grades
Next, determine how many grades you have in your set. In the example above, we have 4 grades.
- Calculate the mean
Now, divide the total sum of the grades by the total number of grades. Using our previous total, the formula will look like this:
$$ \bar{x} = \frac{\text{Total}}{\text{Number of grades}} $$
Using our example numbers, it would be:
$$ \bar{x} = \frac{339}{4} $$
- Simplify the result
Finally, compute the mean by simplifying the equation.
$$ \bar{x} = 84.75 $$
The mean grade is $84.75$.
More Information
The mean grade is a useful measure of central tendency that provides an overview of the average performance in a set of data. It can help identify overall trends in grades.
Tips
- Forgetting to sum all the grades, which can lead to an inaccurate mean.
- Miscounting the number of grades can also lead to an incorrect result.
- Not changing similar grades (like receiving eight 85's) before doing the calculations.
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