Suppose that 40 students take a quiz and everyone in the class scores an 80.
The standard deviation of scores for this quiz is:
80
2
0
0 because if all scores are 80 the mean is 80 and all values are 80 so there is no spread in the data.
Well, if everyone in the class scored an 80 on the quiz, that means there's no variation in the scores. So the standard deviation would be 0. It's like a world full of students who are all equally average. Quite a remarkable feat, I must say!
To calculate the standard deviation of scores, you will need to follow these steps:
1. Find the mean (average) of the scores.
2. Subtract the mean from each individual score.
3. Square each of the differences obtained in step 2.
4. Find the mean (average) of the squared differences.
5. Take the square root of the mean obtained in step 4.
Let's apply these steps to the given scenario:
Step 1: Find the mean (average) of the scores.
Since all 40 students scored an 80, the mean is 80.
Step 2: Subtract the mean from each individual score.
For each student, subtract 80 from 80. The result will always be 0.
Step 3: Square each of the differences obtained in step 2.
Since all differences are 0, any number squared is still 0.
Step 4: Find the mean (average) of the squared differences.
The mean of a set of numbers consisting only of zeros is 0.
Step 5: Take the square root of the mean obtained in step 4.
The square root of 0 is also 0.
Therefore, the standard deviation of the scores is 0.