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Chapter 13: Problem 93

Ten students take a test and get the following scores: $83, 62,81,77,68,92,88,83,72,\( and \)75 .$ What are the average value, the rms value, and the most probable value, respectively, of these test scores?

Short Answer

Expert verified
Answer: The average value is 78.1, the rms value is approximately 77.6, and the most probable value is 83.

Step by step solution

01

Find the average value

Sum the test scores and divide by the number of students (10): \(\frac{83+62+81+77+68+92+88+83+72+75}{10}\). After calculating, we get an average value of \(\frac{781}{10} = 78.1\).
02

Find the rms value

Square each test score, sum the squared scores, and divide the result by the number of students (10): \(\frac{83^2+62^2+81^2+77^2+68^2+92^2+88^2+83^2+72^2+75^2}{10}\). After calculating, we get \(\frac{60,149}{10}\). Take the square root of the result: \(\sqrt{6014.9} \approx 77.6\).
03

Find the most probable value (mode)

To find the most probable value, find the test score that appears most frequently. From the given scores, we observe that the number 83 appears twice, while all other scores appear only once. Therefore, the most probable value (mode) is 83. In summary, the average value is 78.1, the rms value is approximately 77.6, and the most probable value is 83.

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