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In a teacher’s life science course, one student had a test average of "A," a lab work average of "F," and received a "B" for his course grade. Another student’s test average was "F" with a lab work average of "A" and her course grade was a "D." How was this possible? Your challenge is to investigate the concept of a weighted average and see how this teacher was correct in calculating the grades of these two students.

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What are the two major types of statistics?

Statistics can be divided into two major categories, descriptive and inferential. Descriptive statistics provide information about data, without drawing any conclusions about the data. The mode, median, mean, and frequency distribution are all examples of different ways data can be described. Inferential statistics are used to make decisions about the data. Correlation, student's t-test, and the analysis of variance are all examples of inferential statistics. The results of these statistical tests can be used to determine if relationships exist between variables of interest.

What is an average?

The average, also called the mean, is a descriptive statistics used to state a measure of the central tendency of a data set. The average is calculated by adding up all of the values in a data set, then dividing by the number of values in the data set.

What is a weighted average?

In a normal average calculation, an assumption is made that all of the values in the data set have equal value. However, in some cases this is not correct. A weighted average gives the ability to "give more worth" to some of the values in a data set more than others in terms of the total sum of the values. For instance, a teacher might feel tests are more important in determining her students' final class grades than laboratory work. She could weight her tests as 80% of the students' final grades and laboratories only 20%.

What is variance?

Variance states the amount of spread in a data set; the greater the spread of the data, the larger the variance. A small variance indicates that the data is clustered mainly around the average. One common measure of variance is the standard deviation.

What are some common applications of weighted averages?

The Olympics are a great example of the importance of using weighted averages. Let's say that a gymnast from the U.S. was competing and was being judged on her performance by three judges, one from the U.S. and two from other countries. The U.S. judge might be biased, want his fellow American to win the gold medal, and might award her performance a higher score than she deserved. Using weighted averages could reduce this bias if the U.S. judge only accounted for 20% of the gymnast's total score and the other two judges each awarded 40% of her total score. This method could be used to reduce scoring bias on the part of Olympic judges.


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