Question

Ten students take a 100 -point exam. Their grades are 25,97,95,100 , \(35,32,92,75,78,\) and 34 points. The average grade and the rms grade are, respectively, a) 50.0 and 25.0 . c) 77.1 and 19.3 . e) 66.3 and 72.6 . b) 66.7 and 33.3 . d) 37.8 and 76.2 .

Short answer

Answer: e) 66.3 and 72.6

Step-by-step solution

Find the sum of the exam scores

To find the average grade, we first need to find the sum of all exam scores. Add up the given scores: 25 + 97 + 95 + 100 + 35 + 32 + 92 + 75 + 78 + 34

Calculate the average grade

Next, we'll divide the sum of the exam scores by the total number of students (which is 10 in this case) to find the average grade: (25 + 97 + 95 + 100 + 35 + 32 + 92 + 75 + 78 + 34)/10 = 66.3

Calculate the sum of the squared exam scores

To find the rms grade, we need to calculate the sum of the squared exam scores. Square each exam score and add them up: (25^2 + 97^2 + 95^2 + 100^2 + 35^2 + 32^2 + 92^2 + 75^2 + 78^2 + 34^2)

Calculate the average of the squared exam scores

Next, we will divide the sum of squared exam scores by the total number of students (which is 10 in this case): (25^2 + 97^2 + 95^2 + 100^2 + 35^2 + 32^2 + 92^2 + 75^2 + 78^2 + 34^2) / 10

Calculate the rms grade

Now, we will find the square root of the average of squared exam scores to get the rms grade: √[(25^2 + 97^2 + 95^2 + 100^2 + 35^2 + 32^2 + 92^2 + 75^2 + 78^2 + 34^2) / 10]

Compare results to the options given

The average grade we calculated is 66.3, and the rms grade can be found by evaluating the above expression. Based on these calculations, we can compare the results to the given options and select the one that matches our results. The correct answer is option e) 66.3 and 72.6.