In a normal distribution of scores, four participants obtained the following deviation scores: +1, -2, +5, and -10. (a) Which score reflects the highest raw score? (b) Which score reflects the lowest raw score? (c) Rank-order the deviation scores in terms of their frequency, starting with the score with the lowest frequency.
-10 +5 -2 +1
To answer these questions, we need to understand deviation scores and their relationship with raw scores in a normal distribution.
A deviation score represents how far a particular score is from the mean of the distribution. It is calculated by subtracting the mean from the raw score. Let's calculate the raw scores using the given deviation scores:
Mean = (1 - 2 + 5 - 10) / 4 = -6 / 4 = -1.5
(a) To find the highest raw score, we need to add the mean to the deviation score that reflects the highest value. So, +5 (the highest deviation score) + (-1.5) = 3.5. Therefore, the highest raw score is 3.5.
(b) To find the lowest raw score, we perform the same calculation. -10 (the lowest deviation score) + (-1.5) = -11.5. Therefore, the lowest raw score is -11.5.
(c) To rank-order the deviation scores based on their frequency, we count the number of times each deviation score appears:
+1: Appears once
-2: Appears once
+5: Appears once
-10: Appears once
Since each deviation score appears only once, they all have the same frequency. Therefore, in terms of frequency, the rank order of the deviation scores would be: +1, -2, +5, -10.
Now you know how to find the highest and lowest raw scores from deviation scores in a normal distribution, as well as how to rank the deviation scores based on their frequency.