Suppose you want to calculate how far each student was from the mean in exam 1 and store it in a column called deviation. Which of the following is a correct way to do so?

Question

BlackTom AI · Accepted Answer

We start by restating the scenario and the available options to compare them clearly.
Question: Suppose you want to calculate how far each student was from the mean in exam 1 and store it in a column called deviation. Which of the following is a correct way to do so?
Answer options:
1) grades$deviation <- mean(grades$exam1)
2) grades$exam1 <- mean(grades$exam1)
3) grades$exam1 <- mean(grades$exam1) - grades$exam1
4) grades$deviation <- grades$exam1 - mean(grades$exam1)

Now, evaluate each option step by step:
Option 1: grades$deviation <- mean(grades$exam1)
- This assigns the scalar mean value of exam1 to every element in the deviation column. It does not compute the difference between each student's score and the mean, so it fails to reflect how far each student is from the mean. It ignores the actual exam1 scores on a per-student basis and simply replicates the mean.
- Conceptual flaw: treating deviation as a constant equal to the mean rather than a per-row difference.

Option 2: grades$exam1 <- mean(grades$exam1)
- This operation overwrites the original exam1 scores with the overall mean, replacing each student’s score with the same fixed value. It does not create a deviation column, and it permanently erases the individual scores required to compute deviations.
- Conceptual flaw: mutation of the original data in a way that destroys per-student information and does not produce the requested deviation column.

Option 3: grades$exam1 <- mean(grades$exam1) - grades$exam1
- Here, the mean is subtracted from each student’s exam1 value, but in the reverse order: it computes mean minus score. While this yields a difference from the mean, it produces the absolute value of the difference with a reversed sign for each case (and in fact yields negative numbers for scores above the mean). It does not create a deviation column named appropriately and misrepresents the direction of deviation.
- Conceptual flaw: wrong subtraction order and interpretation of deviation; also it overwrites the exam1 column instead of creating a new deviation column.

Option 4: grades$deviation <- grades$exam1 - mean(grades$exam1)
- This option computes, for each student, the difference between their score on exam1 and the overall mean, which is precisely the deviation from the mean. It stores the result in a new column named deviation, preserving the original exam1 scores unmodified. This aligns with the goal of capturing how far each student is from the mean, with sign indicating whether below or above average.
- Correct application: per-row difference between exam1 and the mean, saved to a dedicated deviation column, without altering the original data structure unnecessarily.

In summary, the key criteria are: (a) compute the per-student difference from the mean, (b) store it in a new column named deviation, and (c) avoid overwriting the original exam scores. Option 4 satisfies all of these requirements, while options 1–3 fail in one or more of these aspects.

ECON3310001.1251 Quiz 3: Dataframes

Suppose you want to calculate how far each student was from the mean in exam 1 and store it in a column called deviation. Which of the following is a correct way to do so?

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